Click here for algorithms and associated software appearing

in the book Numerical Methods for Special Functions.

This includes verified software for:

Airy functions

Scorer functions

Prolate spheroidal harmonics

Oblate spheroidal harmonics

Toroidal harmonics

Modified Bessel functions of integer orders

Modified spherical Bessel functions

Modified Bessel functions of purely imaginary order

Parabolic cylinder functions of real order

Scorer functions

Prolate spheroidal harmonics

Oblate spheroidal harmonics

Toroidal harmonics

Modified Bessel functions of integer orders

Modified spherical Bessel functions

Modified Bessel functions of purely imaginary order

Parabolic cylinder functions of real order

Zeros of first kind Bessel functions

Additional published software:

Parabolic cylinder function W(a,x) and its derivative

Laguerre polynomials

Conical function (see update here)

A new Fortran code to compute Legendre functions

Computation and inversion of the gamma cumulative distribution (central and non-central)

This package includes the computation and inversion of Marcum functions as well as other

functions which are used in this computation: gamma function, logarithm of the gamma

function, regulated gamma function, error function...

Laguerre polynomials

Conical function (see update here)

A new Fortran code to compute Legendre functions

Computation and inversion of the gamma cumulative distribution (central and non-central)

This package includes the computation and inversion of Marcum functions as well as other

functions which are used in this computation: gamma function, logarithm of the gamma

function, regulated gamma function, error function...

Software under development:

Gaussian quadrature

(Gauss Hermire and Gauss-Laguerre so far)

Zeros of general Bessel functions and of their derivatives (including mixed derivatives)

[Preliminary codes]

Complex zeros of second order ODEs (Bessel, parabolic cylinder functions, Bessel polynomials)

[Preliminary Maple worksheets]

(Gauss Hermire and Gauss-Laguerre so far)

Zeros of general Bessel functions and of their derivatives (including mixed derivatives)

[Preliminary codes]

Complex zeros of second order ODEs (Bessel, parabolic cylinder functions, Bessel polynomials)

[Preliminary Maple worksheets]