NAME
PDL::GSL::SF - PDL interface to GSL Special Functions
DESCRIPTION
This is an interface to the Special Function package present in the GNU Scientific Library.
FUNCTIONS
gsl_sf_airy_Ai
Signature: (double x(); double [o]y(); double [o]e())Airy Function Ai(x).
gsl_sf_airy_Ai does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_airy_Bi
Signature: (double x(); double [o]y(); double [o]e())Airy Function Bi(x).
gsl_sf_airy_Bi does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_airy_Ai_scaled
Signature: (double x(); double [o]y(); double [o]e())Scaled Airy Function Ai(x). Ai(x) for x < 0 and exp(+2/3 x^{3/2}) Ai(x) for x > 0.
gsl_sf_airy_Ai_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_airy_Bi_scaled
Signature: (double x(); double [o]y(); double [o]e())Scaled Airy Function Bi(x). Bi(x) for x < 0 and exp(+2/3 x^{3/2}) Bi(x) for x > 0.
gsl_sf_airy_Bi_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_airy_Ai_deriv
Signature: (double x(); double [o]y(); double [o]e())Derivative Airy Function Ai`(x).
gsl_sf_airy_Ai_deriv does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_airy_Bi_deriv
Signature: (double x(); double [o]y(); double [o]e())Derivative Airy Function Bi`(x).
gsl_sf_airy_Bi_deriv does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_airy_Ai_deriv_scaled
Signature: (double x(); double [o]y(); double [o]e())Derivative Scaled Airy Function Ai(x). Ai`(x) for x < 0 and exp(+2/3 x^{3/2}) Ai`(x) for x > 0.
gsl_sf_airy_Ai_deriv_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_airy_Bi_deriv_scaled
Signature: (double x(); double [o]y(); double [o]e())Derivative Scaled Airy Function Bi(x). Bi`(x) for x < 0 and exp(+2/3 x^{3/2}) Bi`(x) for x > 0.
gsl_sf_airy_Bi_deriv_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_Jn
Signature: (double x(); double [o]y(); double [o]e(); int n)Regular Bessel Function J_n(x).
gsl_sf_bessel_Jn does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_Jn_array
Signature: (double x(); double [o]y(num); int s; IV n=>num)Array of Regular Bessel Functions J_{s}(x) to J_{s+n-1}(x).
gsl_sf_bessel_Jn_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_Yn
Signature: (double x(); double [o]y(); double [o]e(); int n)IrRegular Bessel Function Y_n(x).
gsl_sf_bessel_Yn does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_Yn_array
Signature: (double x(); double [o]y(num); int s; IV n=>num)Array of Regular Bessel Functions Y_{s}(x) to Y_{s+n-1}(x).
gsl_sf_bessel_Yn_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_In
Signature: (double x(); double [o]y(); double [o]e(); int n)Regular Modified Bessel Function I_n(x).
gsl_sf_bessel_In does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_I_array
Signature: (double x(); double [o]y(num); int s; IV n=>num)Array of Regular Modified Bessel Functions I_{s}(x) to I_{s+n-1}(x).
gsl_sf_bessel_I_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_In_scaled
Signature: (double x(); double [o]y(); double [o]e(); int n)Scaled Regular Modified Bessel Function exp(-|x|) I_n(x).
gsl_sf_bessel_In_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_In_scaled_array
Signature: (double x(); double [o]y(num); int s; IV n=>num)Array of Scaled Regular Modified Bessel Functions exp(-|x|) I_{s}(x) to exp(-|x|) I_{s+n-1}(x).
gsl_sf_bessel_In_scaled_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_Kn
Signature: (double x(); double [o]y(); double [o]e(); int n)IrRegular Modified Bessel Function K_n(x).
gsl_sf_bessel_Kn does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_K_array
Signature: (double x(); double [o]y(num); int s; IV n=>num)Array of IrRegular Modified Bessel Functions K_{s}(x) to K_{s+n-1}(x).
gsl_sf_bessel_K_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_Kn_scaled
Signature: (double x(); double [o]y(); double [o]e(); int n)Scaled IrRegular Modified Bessel Function exp(-|x|) K_n(x).
gsl_sf_bessel_Kn_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_Kn_scaled_array
Signature: (double x(); double [o]y(num); int s; IV n=>num)Array of Scaled IrRegular Modified Bessel Functions exp(-|x|) K_{s}(x) to exp(-|x|) K_{s+n-1}(x).
gsl_sf_bessel_Kn_scaled_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_jl
Signature: (double x(); double [o]y(); double [o]e(); int n)Regular Sphericl Bessel Function J_n(x).
gsl_sf_bessel_jl does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_jl_array
Signature: (double x(); double [o]y(num); int n=>num)Array of Spherical Regular Bessel Functions J_{0}(x) to J_{n-1}(x).
gsl_sf_bessel_jl_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_yl
Signature: (double x(); double [o]y(); double [o]e(); int n)IrRegular Spherical Bessel Function y_n(x).
gsl_sf_bessel_yl does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_yl_array
Signature: (double x(); double [o]y(num); int n=>num)Array of Regular Spherical Bessel Functions y_{0}(x) to y_{n-1}(x).
gsl_sf_bessel_yl_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_il_scaled
Signature: (double x(); double [o]y(); double [o]e(); int n)Scaled Regular Modified Spherical Bessel Function exp(-|x|) i_n(x).
gsl_sf_bessel_il_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_il_scaled_array
Signature: (double x(); double [o]y(num); int n=>num)Array of Scaled Regular Modified Spherical Bessel Functions exp(-|x|) i_{0}(x) to exp(-|x|) i_{n-1}(x).
gsl_sf_bessel_il_scaled_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_kl_scaled
Signature: (double x(); double [o]y(); double [o]e(); int n)Scaled IrRegular Modified Spherical Bessel Function exp(-|x|) k_n(x).
gsl_sf_bessel_kl_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_kl_scaled_array
Signature: (double x(); double [o]y(num); int n=>num)Array of Scaled IrRegular Modified Spherical Bessel Functions exp(-|x|) k_{s}(x) to exp(-|x|) k_{s+n-1}(x).
gsl_sf_bessel_kl_scaled_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_Jnu
Signature: (double x(); double [o]y(); double [o]e(); double n)Regular Cylindrical Bessel Function J_nu(x).
gsl_sf_bessel_Jnu does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_Ynu
Signature: (double x(); double [o]y(); double [o]e(); double n)IrRegular Cylindrical Bessel Function J_nu(x).
gsl_sf_bessel_Ynu does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_Inu_scaled
Signature: (double x(); double [o]y(); double [o]e(); double n)Scaled Modified Cylindrical Bessel Function exp(-|x|) I_nu(x).
gsl_sf_bessel_Inu_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_Inu
Signature: (double x(); double [o]y(); double [o]e(); double n)Modified Cylindrical Bessel Function I_nu(x).
gsl_sf_bessel_Inu does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_Knu_scaled
Signature: (double x(); double [o]y(); double [o]e(); double n)Scaled Modified Cylindrical Bessel Function exp(-|x|) K_nu(x).
gsl_sf_bessel_Knu_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_Knu
Signature: (double x(); double [o]y(); double [o]e(); double n)Modified Cylindrical Bessel Function K_nu(x).
gsl_sf_bessel_Knu does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_bessel_lnKnu
Signature: (double x(); double [o]y(); double [o]e(); double n)Logarithm of Modified Cylindrical Bessel Function K_nu(x).
gsl_sf_bessel_lnKnu does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_clausen
Signature: (double x(); double [o]y(); double [o]e())Clausen Integral. Cl_2(x) := Integrate[-Log[2 Sin[t/2]], {t,0,x}]
gsl_sf_clausen does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_hydrogenicR
Signature: (double x(); double [o]y(); double [o]e(); int n; int l; double z)Normalized Hydrogenic bound states. Radial dipendence.
gsl_sf_hydrogenicR does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_coulomb_wave_FGp_array
Signature: (double x(); double [o]fc(n); double [o]fcp(n); double [o]gc(n); double [o]gcp(n); int [o]ovfw(); double [o]fe(n); double [o]ge(n); double lam_min; IV kmax=>n; double eta)Coulomb wave functions F_{lam_F}(eta,x), G_{lam_G}(eta,x) and their derivatives; lam_G := lam_F - k_lam_G. if ovfw is signaled then F_L(eta,x) = fc[k_L] * exp(fe) and similar. gsl_sf_coulomb_wave_FGp_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_coulomb_wave_sphF_array
Signature: (double x(); double [o]fc(n); int [o]ovfw(); double [o]fe(n); double lam_min; IV kmax=>n; double eta)Coulomb wave function divided by the argument, F(xi, eta)/xi. This is the function which reduces to spherical Bessel functions in the limit eta->0. gsl_sf_coulomb_wave_sphF_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_coulomb_CL_e
Signature: (double L(); double eta(); double [o]y(); double [o]e())Coulomb wave function normalization constant. [Abramowitz+Stegun 14.1.8, 14.1.9].
gsl_sf_coulomb_CL_e does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_coupling_3j
Signature: (ja(); jb(); jc(); ma(); mb(); mc(); double [o]y(); double [o]e())3j Symbols: (ja jb jc) over (ma mb mc).
gsl_sf_coupling_3j does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_coupling_6j
Signature: (ja(); jb(); jc(); jd(); je(); jf(); double [o]y(); double [o]e())6j Symbols: (ja jb jc) over (jd je jf).
gsl_sf_coupling_6j does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_coupling_9j
Signature: (ja(); jb(); jc(); jd(); je(); jf(); jg(); jh(); ji(); double [o]y(); double [o]e())9j Symbols: (ja jb jc) over (jd je jf) over (jg jh ji).
gsl_sf_coupling_9j does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_dawson
Signature: (double x(); double [o]y(); double [o]e())Dawsons integral: Exp[-x^2] Integral[ Exp[t^2], {t,0,x}]
gsl_sf_dawson does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_debye_1
Signature: (double x(); double [o]y(); double [o]e())D_n(x) := n/x^n Integrate[t^n/(e^t - 1), {t,0,x}]
gsl_sf_debye_1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_debye_2
Signature: (double x(); double [o]y(); double [o]e())D_n(x) := n/x^n Integrate[t^n/(e^t - 1), {t,0,x}]
gsl_sf_debye_2 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_debye_3
Signature: (double x(); double [o]y(); double [o]e())D_n(x) := n/x^n Integrate[t^n/(e^t - 1), {t,0,x}]
gsl_sf_debye_3 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_debye_4
Signature: (double x(); double [o]y(); double [o]e())D_n(x) := n/x^n Integrate[t^n/(e^t - 1), {t,0,x}]
gsl_sf_debye_4 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_dilog
Signature: (double x(); double [o]y(); double [o]e())/* Real part of DiLogarithm(x), for real argument. In Lewins notation, this is Li_2(x). Li_2(x) = - Re[ Integrate[ Log[1-s] / s, {s, 0, x}] ]
gsl_sf_dilog does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_complex_dilog
Signature: (double r(); double t(); double [o]re(); double [o]im(); double [o]ere(); double [o]eim())DiLogarithm(z), for complex argument z = r Exp[i theta].
gsl_sf_complex_dilog does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_multiply
Signature: (double x(); double xx(); double [o]y(); double [o]e())Multiplication.
gsl_sf_multiply does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_multiply_err
Signature: (double x(); double xe(); double xx(); double xxe(); double [o]y(); double [o]e())Multiplication with associated errors.
gsl_sf_multiply_err does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_ellint_Kcomp
Signature: (double k(); double [o]y(); double [o]e())Legendre form of complete elliptic integrals K(k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}].
gsl_sf_ellint_Kcomp does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_ellint_Ecomp
Signature: (double k(); double [o]y(); double [o]e())Legendre form of complete elliptic integrals E(k) = Integral[ Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}]
gsl_sf_ellint_Ecomp does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_ellint_F
Signature: (double phi(); double k(); double [o]y(); double [o]e())Legendre form of incomplete elliptic integrals F(phi,k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]
gsl_sf_ellint_F does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_ellint_E
Signature: (double phi(); double k(); double [o]y(); double [o]e())Legendre form of incomplete elliptic integrals E(phi,k) = Integral[ Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]
gsl_sf_ellint_E does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_ellint_P
Signature: (double phi(); double k(); double n();
double [o]y(); double [o]e())Legendre form of incomplete elliptic integrals P(phi,k,n) = Integral[(1 + n Sin[t]^2)^(-1)/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]
gsl_sf_ellint_P does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_ellint_D
Signature: (double phi(); double k();
double [o]y(); double [o]e())Legendre form of incomplete elliptic integrals D(phi,k)
gsl_sf_ellint_D does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_ellint_RC
Signature: (double x(); double yy(); double [o]y(); double [o]e())Carlsons symmetric basis of functions RC(x,y) = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1)], {t,0,Inf}
gsl_sf_ellint_RC does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_ellint_RD
Signature: (double x(); double yy(); double z(); double [o]y(); double [o]e())Carlsons symmetric basis of functions RD(x,y,z) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-3/2), {t,0,Inf}]
gsl_sf_ellint_RD does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_ellint_RF
Signature: (double x(); double yy(); double z(); double [o]y(); double [o]e())Carlsons symmetric basis of functions RF(x,y,z) = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2), {t,0,Inf}]
gsl_sf_ellint_RF does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_ellint_RJ
Signature: (double x(); double yy(); double z(); double p(); double [o]y(); double [o]e())Carlsons symmetric basis of functions RJ(x,y,z,p) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2) (t+p)^(-1), {t,0,Inf}]
gsl_sf_ellint_RJ does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_elljac
Signature: (double u(); double m(); double [o]sn(); double [o]cn(); double [o]dn())Jacobian elliptic functions sn, dn, cn by descending Landen transformations
gsl_sf_elljac does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_erfc
Signature: (double x(); double [o]y(); double [o]e())Complementary Error Function erfc(x) := 2/Sqrt[Pi] Integrate[Exp[-t^2], {t,x,Infinity}]
gsl_sf_erfc does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_log_erfc
Signature: (double x(); double [o]y(); double [o]e())Log Complementary Error Function
gsl_sf_log_erfc does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_erf
Signature: (double x(); double [o]y(); double [o]e())Error Function erf(x) := 2/Sqrt[Pi] Integrate[Exp[-t^2], {t,0,x}]
gsl_sf_erf does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_erf_Z
Signature: (double x(); double [o]y(); double [o]e())Z(x) : Abramowitz+Stegun 26.2.1
gsl_sf_erf_Z does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_erf_Q
Signature: (double x(); double [o]y(); double [o]e())Q(x) : Abramowitz+Stegun 26.2.1
gsl_sf_erf_Q does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_exp
Signature: (double x(); double [o]y(); double [o]e())Exponential
gsl_sf_exp does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_exprel_n
Signature: (double x(); double [o]y(); double [o]e(); int n)N-relative Exponential. exprel_N(x) = N!/x^N (exp(x) - Sum[x^k/k!, {k,0,N-1}]) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1(1,1+N,x)
gsl_sf_exprel_n does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_exp_err
Signature: (double x(); double dx(); double [o]y(); double [o]e())Exponential of a quantity with given error.
gsl_sf_exp_err does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_expint_E1
Signature: (double x(); double [o]y(); double [o]e())E_1(x) := Re[ Integrate[ Exp[-xt]/t, {t,1,Infinity}] ]
gsl_sf_expint_E1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_expint_E2
Signature: (double x(); double [o]y(); double [o]e())E_2(x) := Re[ Integrate[ Exp[-xt]/t^2, {t,1,Infity}] ]
gsl_sf_expint_E2 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_expint_Ei
Signature: (double x(); double [o]y(); double [o]e())Ei(x) := PV Integrate[ Exp[-t]/t, {t,-x,Infinity}]
gsl_sf_expint_Ei does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_Shi
Signature: (double x(); double [o]y(); double [o]e())Shi(x) := Integrate[ Sinh[t]/t, {t,0,x}]
gsl_sf_Shi does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_Chi
Signature: (double x(); double [o]y(); double [o]e())Chi(x) := Re[ M_EULER + log(x) + Integrate[(Cosh[t]-1)/t, {t,0,x}] ]
gsl_sf_Chi does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_expint_3
Signature: (double x(); double [o]y(); double [o]e())Ei_3(x) := Integral[ Exp[-t^3], {t,0,x}]
gsl_sf_expint_3 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_Si
Signature: (double x(); double [o]y(); double [o]e())Si(x) := Integrate[ Sin[t]/t, {t,0,x}]
gsl_sf_Si does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_Ci
Signature: (double x(); double [o]y(); double [o]e())Ci(x) := -Integrate[ Cos[t]/t, {t,x,Infinity}]
gsl_sf_Ci does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_atanint
Signature: (double x(); double [o]y(); double [o]e())AtanInt(x) := Integral[ Arctan[t]/t, {t,0,x}]
gsl_sf_atanint does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_fermi_dirac_int
Signature: (double x(); double [o]y(); double [o]e(); int j)Complete integral F_j(x) for integer j
gsl_sf_fermi_dirac_int does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_fermi_dirac_mhalf
Signature: (double x(); double [o]y(); double [o]e())Complete integral F_{-1/2}(x)
gsl_sf_fermi_dirac_mhalf does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_fermi_dirac_half
Signature: (double x(); double [o]y(); double [o]e())Complete integral F_{1/2}(x)
gsl_sf_fermi_dirac_half does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_fermi_dirac_3half
Signature: (double x(); double [o]y(); double [o]e())Complete integral F_{3/2}(x)
gsl_sf_fermi_dirac_3half does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_fermi_dirac_inc_0
Signature: (double x(); double [o]y(); double [o]e(); double b)Incomplete integral F_0(x,b) = ln(1 + e^(b-x)) - (b-x)
gsl_sf_fermi_dirac_inc_0 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_lngamma
Signature: (double x(); double [o]y(); double [o]s(); double [o]e())Log[Gamma(x)], x not a negative integer Uses real Lanczos method. Determines the sign of Gamma[x] as well as Log[|Gamma[x]|] for x < 0. So Gamma[x] = sgn * Exp[result_lg].
gsl_sf_lngamma does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_gamma
Signature: (double x(); double [o]y(); double [o]e())Gamma(x), x not a negative integer
gsl_sf_gamma does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_gammastar
Signature: (double x(); double [o]y(); double [o]e())Regulated Gamma Function, x > 0 Gamma^*(x) = Gamma(x)/(Sqrt[2Pi] x^(x-1/2) exp(-x)) = (1 + 1/(12x) + ...), x->Inf
gsl_sf_gammastar does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_gammainv
Signature: (double x(); double [o]y(); double [o]e())1/Gamma(x)
gsl_sf_gammainv does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_lngamma_complex
Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())Log[Gamma(z)] for z complex, z not a negative integer. Calculates: lnr = log|Gamma(z)|, arg = arg(Gamma(z)) in (-Pi, Pi]
gsl_sf_lngamma_complex does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_taylorcoeff
Signature: (double x(); double [o]y(); double [o]e(); int n)x^n / n!
gsl_sf_taylorcoeff does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_fact
Signature: (x(); double [o]y(); double [o]e())n!
gsl_sf_fact does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_doublefact
Signature: (x(); double [o]y(); double [o]e())n!! = n(n-2)(n-4)
gsl_sf_doublefact does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_lnfact
Signature: (x(); double [o]y(); double [o]e())ln n!
gsl_sf_lnfact does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_lndoublefact
Signature: (x(); double [o]y(); double [o]e())ln n!!
gsl_sf_lndoublefact does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_lnchoose
Signature: (n(); m(); double [o]y(); double [o]e())log(n choose m)
gsl_sf_lnchoose does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_choose
Signature: (n(); m(); double [o]y(); double [o]e())n choose m
gsl_sf_choose does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_lnpoch
Signature: (double x(); double [o]y(); double [o]s(); double [o]e(); double a)Logarithm of Pochammer (Apell) symbol, with sign information. result = log( |(a)_x| ), sgn = sgn( (a)_x ) where (a)_x := Gamma[a + x]/Gamma[a]
gsl_sf_lnpoch does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_poch
Signature: (double x(); double [o]y(); double [o]e(); double a)Pochammer (Apell) symbol (a)_x := Gamma[a + x]/Gamma[x]
gsl_sf_poch does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_pochrel
Signature: (double x(); double [o]y(); double [o]e(); double a)Relative Pochammer (Apell) symbol ((a,x) - 1)/x where (a,x) = (a)_x := Gamma[a + x]/Gamma[a]
gsl_sf_pochrel does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_gamma_inc_Q
Signature: (double x(); double [o]y(); double [o]e(); double a)Normalized Incomplete Gamma Function Q(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,x,Infinity} ]
gsl_sf_gamma_inc_Q does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_gamma_inc_P
Signature: (double x(); double [o]y(); double [o]e(); double a)Complementary Normalized Incomplete Gamma Function P(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,0,x} ]
gsl_sf_gamma_inc_P does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_lnbeta
Signature: (double a(); double b(); double [o]y(); double [o]e())Logarithm of Beta Function Log[B(a,b)]
gsl_sf_lnbeta does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_beta
Signature: (double a(); double b();double [o]y(); double [o]e())Beta Function B(a,b)
gsl_sf_beta does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_gegenpoly_n
Signature: (double x(); double [o]y(); double [o]e(); int n; double lambda)Evaluate Gegenbauer polynomials.
gsl_sf_gegenpoly_n does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_gegenpoly_array
Signature: (double x(); double [o]y(num); int n=>num; double lambda)Calculate array of Gegenbauer polynomials from 0 to n-1.
gsl_sf_gegenpoly_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_hyperg_0F1
Signature: (double x(); double [o]y(); double [o]e(); double c)/* Hypergeometric function related to Bessel functions 0F1[c,x] = Gamma[c] x^(1/2(1-c)) I_{c-1}(2 Sqrt[x]) Gamma[c] (-x)^(1/2(1-c)) J_{c-1}(2 Sqrt[-x])
gsl_sf_hyperg_0F1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_hyperg_1F1
Signature: (double x(); double [o]y(); double [o]e(); double a; double b)Confluent hypergeometric function for integer parameters. 1F1[a,b,x] = M(a,b,x)
gsl_sf_hyperg_1F1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_hyperg_U
Signature: (double x(); double [o]y(); double [o]e(); double a; double b)Confluent hypergeometric function for integer parameters. U(a,b,x)
gsl_sf_hyperg_U does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_hyperg_2F1
Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)Confluent hypergeometric function for integer parameters. 2F1[a,b,c,x]
gsl_sf_hyperg_2F1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_hyperg_2F1_conj
Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x]
gsl_sf_hyperg_2F1_conj does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_hyperg_2F1_renorm
Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)Renormalized Gauss hypergeometric function 2F1[a,b,c,x] / Gamma[c]
gsl_sf_hyperg_2F1_renorm does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_hyperg_2F1_conj_renorm
Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)Renormalized Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x] / Gamma[c]
gsl_sf_hyperg_2F1_conj_renorm does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_hyperg_2F0
Signature: (double x(); double [o]y(); double [o]e(); double a; double b)Mysterious hypergeometric function. The series representation is a divergent hypergeometric series. However, for x < 0 we have 2F0(a,b,x) = (-1/x)^a U(a,1+a-b,-1/x)
gsl_sf_hyperg_2F0 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_laguerre_n
Signature: (double x(); double [o]y(); double [o]e(); int n; double a)Evaluate generalized Laguerre polynomials.
gsl_sf_laguerre_n does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_legendre_Pl
Signature: (double x(); double [o]y(); double [o]e(); int l)P_l(x)
gsl_sf_legendre_Pl does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_legendre_Pl_array
Signature: (double x(); double [o]y(num); int l=>num)P_l(x) from 0 to n-1.
gsl_sf_legendre_Pl_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_legendre_Ql
Signature: (double x(); double [o]y(); double [o]e(); int l)Q_l(x)
gsl_sf_legendre_Ql does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_legendre_Plm
Signature: (double x(); double [o]y(); double [o]e(); int l; int m)P_lm(x)
gsl_sf_legendre_Plm does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_legendre_array
Signature: (double x(); double [o]y(n=CALC($COMP(lmax)*($COMP(lmax)+1)/2+$COMP(lmax)+1)); double [t]work(wn=CALC(gsl_sf_legendre_array_n($COMP(lmax)))); char norm; int lmax; int csphase)Calculate all normalized associated Legendre polynomials.
$Plm = gsl_sf_legendre_array($x,'P',4,-1);
The calculation is done for degree 0 <= l <= lmax and order 0 <= m <= l on the range abs(x)<=1.
The parameter norm should be:
- 'S' for Schmidt semi-normalized associated Legendre polynomials S_l^m(x),
- 'Y' for spherical harmonic associated Legendre polynomials Y_l^m(x), or
- 'N' for fully normalized associated Legendre polynomials N_l^m(x).
- 'P' (or any other) for unnormalized associated Legendre polynomials P_l^m(x),
lmax is the maximum degree l. csphase should be (-1) to INCLUDE the Condon-Shortley phase factor (-1)^m, or (+1) to EXCLUDE it.
See "gsl_sf_legendre_array_index" to get the value of l and m in the returned vector.
gsl_sf_legendre_array processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_legendre_array_index
Signature: (int [o]l(n=CALC($COMP(lmax)*($COMP(lmax)+1)/2+$COMP(lmax)+1)); int [o]m(n); int lmax)Calculate the relation between gsl_sf_legendre_arrays index and l and m values.
Note that this function is called differently than the corresponding GSL function, to make it more useful for PDL: here you just input the maximum l (lmax) that was used in gsl_sf_legendre_array and it calculates all l and m values.
gsl_sf_legendre_array_index does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_legendre_sphPlm
Signature: (double x(); double [o]y(); double [o]e(); int l; int m)P_lm(x), normalized properly for use in spherical harmonics
gsl_sf_legendre_sphPlm does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_conicalP_half
Signature: (double x(); double [o]y(); double [o]e(); double lambda)Irregular Spherical Conical Function P^{1/2}_{-1/2 + I lambda}(x)
gsl_sf_conicalP_half does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_conicalP_mhalf
Signature: (double x(); double [o]y(); double [o]e(); double lambda)Regular Spherical Conical Function P^{-1/2}_{-1/2 + I lambda}(x)
gsl_sf_conicalP_mhalf does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_conicalP_0
Signature: (double x(); double [o]y(); double [o]e(); double lambda)Conical Function P^{0}_{-1/2 + I lambda}(x)
gsl_sf_conicalP_0 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_conicalP_1
Signature: (double x(); double [o]y(); double [o]e(); double lambda)Conical Function P^{1}_{-1/2 + I lambda}(x)
gsl_sf_conicalP_1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_conicalP_sph_reg
Signature: (double x(); double [o]y(); double [o]e(); int l; double lambda)Regular Spherical Conical Function P^{-1/2-l}_{-1/2 + I lambda}(x)
gsl_sf_conicalP_sph_reg does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_conicalP_cyl_reg_e
Signature: (double x(); double [o]y(); double [o]e(); int m; double lambda)Regular Cylindrical Conical Function P^{-m}_{-1/2 + I lambda}(x)
gsl_sf_conicalP_cyl_reg_e does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_legendre_H3d
Signature: (double [o]y(); double [o]e(); int l; double lambda; double eta)lth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space.
gsl_sf_legendre_H3d does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_legendre_H3d_array
Signature: (double [o]y(num); int l=>num; double lambda; double eta)Array of H3d(ell), for l from 0 to n-1.
gsl_sf_legendre_H3d_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_log
Signature: (double x(); double [o]y(); double [o]e())Provide a logarithm function with GSL semantics.
gsl_sf_log does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_complex_log
Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())Complex Logarithm exp(lnr + I theta) = zr + I zi Returns argument in [-pi,pi].
gsl_sf_complex_log does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_poly_eval
Signature: (double x(); double c(m); double [o]y())c[0] + c[1] x + c[2] x^2 + ... + c[m-1] x^(m-1)
gsl_poly_eval does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_pow_int
Signature: (double x(); double [o]y(); double [o]e(); int n)Calculate x^n.
gsl_sf_pow_int does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_psi
Signature: (double x(); double [o]y(); double [o]e())Di-Gamma Function psi(x).
gsl_sf_psi does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_psi_1piy
Signature: (double x(); double [o]y(); double [o]e())Di-Gamma Function Re[psi(1 + I y)]
gsl_sf_psi_1piy does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_psi_n
Signature: (double x(); double [o]y(); double [o]e(); int n)Poly-Gamma Function psi^(n)(x)
gsl_sf_psi_n does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_synchrotron_1
Signature: (double x(); double [o]y(); double [o]e())First synchrotron function: synchrotron_1(x) = x Integral[ K_{5/3}(t), {t, x, Infinity}]
gsl_sf_synchrotron_1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_synchrotron_2
Signature: (double x(); double [o]y(); double [o]e())Second synchroton function: synchrotron_2(x) = x * K_{2/3}(x)
gsl_sf_synchrotron_2 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_transport_2
Signature: (double x(); double [o]y(); double [o]e())J(2,x)
gsl_sf_transport_2 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_transport_3
Signature: (double x(); double [o]y(); double [o]e())J(3,x)
gsl_sf_transport_3 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_transport_4
Signature: (double x(); double [o]y(); double [o]e())J(4,x)
gsl_sf_transport_4 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_transport_5
Signature: (double x(); double [o]y(); double [o]e())J(5,x)
gsl_sf_transport_5 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_sin
Signature: (double x(); double [o]y(); double [o]e())Sin(x) with GSL semantics.
gsl_sf_sin does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_cos
Signature: (double x(); double [o]y(); double [o]e())Cos(x) with GSL semantics.
gsl_sf_cos does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_hypot
Signature: (double x(); double xx(); double [o]y(); double [o]e())Hypot(x,xx) with GSL semantics.
gsl_sf_hypot does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_complex_sin
Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())Sin(z) for complex z
gsl_sf_complex_sin does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_complex_cos
Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())Cos(z) for complex z
gsl_sf_complex_cos does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_complex_logsin
Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())Log(Sin(z)) for complex z
gsl_sf_complex_logsin does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_lnsinh
Signature: (double x(); double [o]y(); double [o]e())Log(Sinh(x)) with GSL semantics.
gsl_sf_lnsinh does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_lncosh
Signature: (double x(); double [o]y(); double [o]e())Log(Cos(x)) with GSL semantics.
gsl_sf_lncosh does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_polar_to_rect
Signature: (double r(); double t(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())Convert polar to rectlinear coordinates.
gsl_sf_polar_to_rect does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_rect_to_polar
Signature: (double x(); double y(); double [o]r(); double [o]t(); double [o]re(); double [o]te())Convert rectlinear to polar coordinates. return argument in range [-pi, pi].
gsl_sf_rect_to_polar does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_angle_restrict_symm
Signature: (double [o]y())Force an angle to lie in the range (-pi,pi].
gsl_sf_angle_restrict_symm does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_angle_restrict_pos
Signature: (double [o]y())Force an angle to lie in the range [0,2 pi).
gsl_sf_angle_restrict_pos does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_sin_err
Signature: (double x(); double dx(); double [o]y(); double [o]e())Sin(x) for quantity with an associated error.
gsl_sf_sin_err does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_cos_err
Signature: (double x(); double dx(); double [o]y(); double [o]e())Cos(x) for quantity with an associated error.
gsl_sf_cos_err does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_zeta
Signature: (double x(); double [o]y(); double [o]e())Riemann Zeta Function zeta(x) = Sum[ k^(-s), {k,1,Infinity} ], s != 1.0
gsl_sf_zeta does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_hzeta
Signature: (double s(); double [o]y(); double [o]e(); double q)Hurwicz Zeta Function zeta(s,q) = Sum[ (k+q)^(-s), {k,0,Infinity} ]
gsl_sf_hzeta does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
gsl_sf_eta
Signature: (double x(); double [o]y(); double [o]e())Eta Function eta(s) = (1-2^(1-s)) zeta(s)
gsl_sf_eta does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
AUTHOR
This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it> All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file.
The GSL SF modules were written by G. Jungman.