gsl
Octave bindings to the GNU Scientific Library
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Computes the Airy function Ai(x) with an accuracy specified by mode.
Computes the Airy function derivative Ai'(x) with an accuracy specified by mode.
Computes the derivative of the scaled Airy function S_A(x) Ai(x).
Computes a scaled version of the Airy function S_A(x) Ai(x).
Computes the Airy function Bi(x) with an accuracy specified by mode.
Computes the Airy function derivative Bi'(x) with an accuracy specified by mode.
Computes the derivative of the scaled Airy function S_B(x) Bi(x).
Computes a scaled version of the Airy function S_B(x) Bi(x).
Computes the location of the s-th zero of the Airy function Ai(x).
Computes the location of the s-th zero of the Airy function derivative Ai(x).
Computes the location of the s-th zero of the Airy function Bi(x).
Computes the location of the s-th zero of the Airy function derivative Bi(x).
Computes the Arctangent integral AtanInt(x) = \int_0^x dt \arctan(t)/t.
Computes the scaled regular modified spherical Bessel function of order l, \exp(-|x|) i_l(x)
This routine computes the values of the scaled regular modified spherical Bessel functions \exp(-|x|) i_l(x) for l from 0 to lmax inclusive for lmax >= 0.
Computes the regular modified cylindrical Bessel function of order n, I_n(x).
his routine computes the values of the regular modified cylindrical Bessel functions I_n(x) for n from nmin to nmax inclusive.
Computes the scaled regular modified cylindrical Bessel function of order n, \exp(-|x|) I_n(x)
This routine computes the values of the scaled regular cylindrical Bessel functions \exp(-|x|) I_n(x) for n from nmin to nmax inclusive.
Computes the regular modified Bessel function of fractional order nu, I_\nu(x) for x>0, \nu>0.
Computes the scaled regular modified Bessel function of fractional order nu, \exp(-|x|)I_\nu(x) for x>0, \nu>0.
Computes the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0.
Computes the values of the regular spherical Bessel functions j_l(x) for l from 0 to lmax inclusive for lmax >= 0 and x >= 0.
This routine uses Steed’s method to compute the values of the regular spherical Bessel functions j_l(x) for l from 0 to lmax inclusive for lmax >= 0 and x >= 0.
Computes the regular cylindrical Bessel function of order n, J_n(x).
This routine computes the values of the regular cylindrical Bessel functions J_n(x) for n from nmin to nmax inclusive.
Computes the regular cylindrical Bessel function of fractional order nu, J_\nu(x).
Computes the scaled irregular modified spherical Bessel function of order l, \exp(x) k_l(x), for x>0.
This routine computes the values of the scaled irregular modified spherical Bessel functions \exp(x) k_l(x) for l from 0 to lmax inclusive for lmax >= 0 and x>0.
Computes the irregular modified cylindrical Bessel function of order n, K_n(x), for x > 0.
This routine computes the values of the irregular modified cylindrical Bessel functions K_n(x) for n from nmin to nmax inclusive.
ERR contains an estimate of the absolute error in the value Z.
This routine computes the values of the scaled irregular cylindrical Bessel functions \exp(x) K_n(x) for n from nmin to nmax inclusive.
Computes the irregular modified Bessel function of fractional order nu, K_\nu(x) for x>0, \nu>0.
Computes the scaled irregular modified Bessel function of fractional order nu, \exp(+|x|) K_\nu(x) for x>0, \nu>0.
Computes the logarithm of the irregular modified Bessel function of fractional order nu, \ln(K_\nu(x)) for x>0, \nu>0.
Computes the irregular spherical Bessel function of order l, y_l(x), for l >= 0.
This routine computes the values of the irregular spherical Bessel functions y_l(x) for l from 0 to lmax inclusive for lmax >= 0.
Computes the irregular cylindrical Bessel function of order n, Y_n(x), for x>0.
This routine computes the values of the irregular cylindrical Bessel functions Y_n(x) for n from nmin to nmax inclusive.
Computes the irregular cylindrical Bessel function of fractional order nu, Y_\nu(x).
Computes the location of the s-th positive zero of the Bessel function J_0(x).
Computes the location of the s-th positive zero of the Bessel function J_1(x).
Computes the location of the n-th positive zero of the Bessel function J_x().
Computes the Beta Function, B(a,b) = \Gamma(a)\Gamma(b)/\Gamma(a+b) for a > 0, b > 0.
Computes the normalized incomplete Beta function
Computes the integral
Computes the combinatorial factor n choose m = n!/(m!(n-m)!).
Computes the Cosine integral Ci(x) = -\int_x^\infty dt \cos(t)/t for x > 0.
The Clausen function is defined by the following integral,
Computes the conical function P^0_{-1/2 + i \lambda}(x) for x > -1.
Computes the conical function P^1_{-1/2 + i \lambda}(x) for x > -1.
Computes the Regular Cylindrical Conical Function P^{-m}_{-1/2 + i \lambda}(x), for x > -1, m >= -1.
Computes the irregular Spherical Conical Function P^{1/2}_{-1/2 + i \lambda}(x) for x > -1.
Computes the regular Spherical Conical Function P^{-1/2}_{-1/2 + i \lambda}(x) for x > -1.
Computes the Regular Spherical Conical Function P^{-1/2-l}_{-1/2 + i \lambda}(x), for x > -1, l >= -1.
computes the Wigner 3-j coefficient,
computes the Wigner 6-j coefficient,
computes the Wigner 9-j coefficient,
The Dawson integral is defined by \exp(-x^2) \int_0^x dt \exp(t^2).
The Debye functions are defined by the integral
The Debye functions are defined by the integral
The Debye functions are defined by the integral
The Debye functions are defined by the integral
The Debye functions are defined by the integral
The Debye functions are defined by the integral
Computes the dilogarithm for a real argument.
Compute the double factorial n!! = n(n-2)(n-4)\dots.
This function computes the incomplete elliptic integral D(\phi,k) which is defined through the Carlson form RD(x,y,z) by the following relation,
This routine computes the elliptic integral E(\phi,k) to the accuracy specified by the mode variable mode.
Computes the complete elliptic integral E(k) to the accuracy specified by the mode variable mode.
This routine computes the elliptic integral F(\phi,k) to the accuracy specified by the mode variable mode.
Computes the complete elliptic integral K(k) pi --- 2 /
This routine computes the incomplete elliptic integral \Pi(\phi,k,n) to the accuracy specified by the mode variable mode.
Computes the complete elliptic integral \Pi(k,n) to the accuracy specified by the mode variable mode.
This routine computes the incomplete elliptic integral RC(x,y) to the accuracy specified by the mode variable mode.
This routine computes the incomplete elliptic integral RD(x,y,z) to the accuracy specified by the mode variable mode.
This routine computes the incomplete elliptic integral RF(x,y,z) to the accuracy specified by the mode variable mode.
This routine computes the incomplete elliptic integral RJ(x,y,z,p) to the accuracy specified by the mode variable mode.
Computes the error function erf(x) = (2/\sqrt(\pi)) \int_0^x dt \exp(-t^2).
Computes the complementary error function erfc(x) = 1 - erf(x) = (2/\sqrt(\pi)) \int_x^\infty \exp(-t^2).
Computes the upper tail of the Gaussian probability function Q(x) = (1/(2\pi)) \int_x^\infty dt \exp(-t^2/2).
Computes the Gaussian probability function Z(x) = (1/(2\pi)) \exp(-x^2/2).
Computes the eta function \eta(s) for arbitrary s.
Computes the eta function \eta(n) for integer n.
Computes the exponential integral Ei_3(x) = \int_0^x dt \exp(-t^3) for x >= 0.
Computes the exponential integral E_1(x),
Computes the second-order exponential integral E_2(x),
Computes the exponential integral E_i(x),
Computes the quantity \exp(x)-1 using an algorithm that is accurate for small x.
These routines exponentiate x and multiply by the factor y to return the product y \exp(x).
Computes the quantity (\exp(x)-1)/x using an algorithm that is accurate for small x.
Computes the quantity 2(\exp(x)-1-x)/x^2 using an algorithm that is accurate for small x.
Computes the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2.
Computes the factorial n!.
Computes the complete Fermi-Dirac integral F_{1/2}(x).
Computes the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \ln(1 + e^{b-x}) - (b-x).
Computes the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\Gamma(j+1)) \int_0^\infty dt (t^j /(\exp(t-x)+1)).
Computes the complete Fermi-Dirac integral F_{-1/2}(x).
Computes the Gamma function \Gamma(x), subject to x not being a negative integer.
These functions compute the incomplete Gamma Function the normalization factor included in the previously defined functions: \Gamma(a,x) = \int_x\infty dt t^{a-1} \exp(-t) for a real and x >= 0.
Computes the complementary normalized incomplete Gamma Function P(a,x) = 1/\Gamma(a) \int_0^x dt t^{a-1} \exp(-t) for a > 0, x >= 0.
Computes the normalized incomplete Gamma Function Q(a,x) = 1/\Gamma(a) \int_x\infty dt t^{a-1} \exp(-t) for a > 0, x >= 0.
Computes the reciprocal of the gamma function, 1/\Gamma(x) using the real Lanczos method.
Computes the regulated Gamma Function \Gamma^*(x) for x > 0.
This function computes an array of Gegenbauer polynomials C^{(\lambda)}_n(x) for n = 0, 1, 2, \dots, nmax, subject to \lambda > -1/2, nmax >= 0.
These functions evaluate the Gegenbauer polynomial C^{(\lambda)}_n(x) for n, lambda, x subject to \lambda > -1/2, n >= 0.
The hazard function for the normal distrbution, also known as the inverse Mill\'s ratio, is defined as h(x) = Z(x)/Q(x) = \sqrt{2/\pi \exp(-x^2 / 2) / \erfc(x/\sqrt 2)}.
This routine computes the n-th normalized hydrogenic bound state radial wavefunction,
Computes the hypergeometric function 0F1(c,x).
Primary Confluent Hypergoemetric U function A&E 13.1.3 All inputs are double as is the output.
Primary Confluent Hypergoemetric U function A&E 13.1.3 m and n are integers.
Computes the hypergeometric function 2F0(a,b,x).
Computes the Gauss hypergeometric function 2F1(a,b,c,x) = F(a,b,c,x) for |x| < 1.
Secondary Confluent Hypergoemetric U function A&E 13.1.3 All inputs are double as is the output.
Secondary Confluent Hypergoemetric U function A&E 13.1.3 m and n are integers.
Computes the Hurwitz zeta function \zeta(s,q) for s > 1, q > 0.
Computes the generalized Laguerre polynomial L^a_n(x) for a > -1 and n >= 0.
These compute the principal branch of the Lambert W function, W_0(x).
These compute the secondary real-valued branch of the Lambert W function, W_{-1}(x).
Calculate all normalized associated Legendre polynomials for 0 <= l <= lmax and 0 <= m <= l for |x| <= 1.
Calculate all normalized associated Legendre polynomials and their first derivatives for 0 <= l <= lmax and 0 <= m <= l for |x| <= 1.
These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1
These functions compute arrays of Legendre polynomials P_l(x) and derivatives dP_l(x)/dx, for l = 0, \dots, lmax, |x| <= 1.
Computes the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1.
Compute arrays of Legendre polynomials P_l^m(x) for m >= 0, l = |m|, ..., lmax, |x| <= 1.
Compute arrays of Legendre polynomials P_l^m(x) and derivatives dP_l^m(x)/dx for m >= 0, l = |m|, ..., lmax, |x| <= 1.
Computes the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0.
Computes the normalized associated Legendre polynomial $\sqrt{(2l+1)/(4\pi)} \sqrt{(l-m)!/(l+m)!} P_l^m(x)$ suitable for use in spherical harmonics.
Computes an array of normalized associated Legendre functions sqrt((2l+1)/(4*pi)) * sqrt((l-m)!/(l+m)!) Plm (x) for m >= 0, l = |m|, ..., lmax, |x| <= 1.0
Computes an array of normalized associated Legendre functions sqrt((2l+1)/(4*pi)) * sqrt((l-m)!/(l+m)!) Plm (x) for m >= 0, l = |m|, ..., lmax, |x| <= 1.0 and their derivatives.
Computes the logarithm of the Beta Function, \log(B(a,b)) for a > 0, b > 0.
Computes the logarithm of n choose m.
Computes \log(\cosh(x)) for any x.
Computes the logarithm of the double factorial of n, \log(n!!).
Computes the logarithm of the factorial of n, \log(n!).
Computes the logarithm of the Gamma function, \log(\Gamma(x)), subject to x not a being negative integer.
Computes the logarithm of the Pochhammer symbol, \log((a)_x) = \log(\Gamma(a + x)/\Gamma(a)) for a > 0, a+x > 0.
Computes \log(\sinh(x)) for x > 0.
Computes \log(1 + x) for x > -1 using an algorithm that is accurate for small x.
Computes \log(1 + x) - x for x > -1 using an algorithm that is accurate for small x.
Computes the logarithm of the complementary error function \log(\erfc(x)).
Computes the characteristic values a_n(q) of the Mathieu function ce_n(q,x).
Computes the characteristic values b_n(q) of the Mathieu function se_n(q,x).
This routine computes the angular Mathieu function ce_n(q,x).
This routine computes the radial j-th kind Mathieu function Mc_n^{(j)}(q,x) of order n.
This routine computes the radial j-th kind Mathieu function Ms_n^{(j)}(q,x) of order n.
This routine computes the angular Mathieu function se_n(q,x).
Computes the Pochhammer symbol
Computes the relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)_x := \Gamma(a + x)/\Gamma(a).
Computes the digamma function \psi(x) for general x, x \ne 0.
Computes the Trigamma function \psi(n) for positive integer n.
Computes the real part of the digamma function on the line 1+i y, Re[\psi(1 + i y)].
Computes the polygamma function \psi^{(m)}(x) for m >= 0, x > 0.
Computes the integral Shi(x) = \int_0^x dt \sinh(t)/t.
Computes the Sine integral Si(x) = \int_0^x dt \sin(t)/t.
Computes \sinc(x) = \sin(\pi x) / (\pi x) for any value of x.
Computes the first synchrotron function x \int_x^\infty dt K_{5/3}(t) for x >= 0.
Computes the second synchrotron function x K_{2/3}(x) for x >= 0.
Computes the Taylor coefficient x^n / n! for x >= 0, n >= 0.
Computes the transport function J(2,x).
Computes the transport function J(3,x).
Computes the transport function J(4,x).
Computes the transport function J(5,x).
Computes the Riemann zeta function \zeta(s) for arbitrary s, s \ne 1.
Computes the Riemann zeta function \zeta(n) for integer n, n \ne 1.
Computes \zeta(s) - 1 for arbitrary s, s \ne 1, where \zeta denotes the Riemann zeta function.
Computes \zeta(s) - 1 for integer n, n \ne 1, where \zeta denotes the Riemann zeta function.
Computes the Riemann zeta function \zeta(s) for arbitrary s, s \ne 1.
gsl_sf is an oct-file containing Octave bindings to the special functions of the GNU Scientific Library (GSL).
Package: gsl