## Computation of Special Functions

version 1.0.0.0 (139 KB) by
MATLAB translation (via f2matlab) of the original FORTRAN of "Computation of Special Functions."

Updated 14 Apr 2005

MATLAB routines for computation of Special Functions

These routines are a direct translation, performed using f2matlab, of the original FORTRAN-77 implementation of "Computation of Special Functions."

For detailed description of the algorithm of each program, please consult the book "Computation of Special Functions."
Also see Errata at:
http://ceta.mit.edu/comp_spec_func/

Bernoulli numbers
Euler numbers
Chebyshev, Laguerre, and Hermite polynomials
Gauss-Laguerre
Gauss-Hermite
gamma function.
logarithm of the gamma function.
gamma function with a complex argument.
beta function.
psi function.
psi function with a complex argument.
incomplete gamma function.
incomplete beta function.
Legendre polynomials
Legendre functions of the second kind
associated Legendre polynomials
Bessel functions of the first and second kinds
zeros of the Bessel functions of the first and second kinds
lambda functions
modified Bessel functions of the first and second kinds
Hankel functions of the first and second kinds
integral of Bessel functions J0(t) and Y0(t) from 0 to x
integral of [1-J0(t)]/t from 0 to x and Y0(t)/t from x to infinity
integral of modified Bessel functions I0(t) and K0(t) from 0 to x
integral of [1-I0(t)]/t from 0 to x and K0(t) from x to infinity
spherical Bessel functions of the first and second kinds
Riccati-Bessel functions of the first kind and second kind
modified spherical Bessel functions of the first kind and second kind
Kelvin functions
zeros of the Kelvin functions
Airy functions
integral of the Airy functions.
zeros of Airy functions
Struve functions with an arbitrary order
integral of Struve function H0(t) from 0 to x.
integral of H0(t)/t from x to infinity.
modified Struve function with an arbitrary order.
integral of modified Struve function L0(t) from 0 to x.
hypergeometric function
hypergeometric function M(a,b,z)
hypergeometric function U(a,b,x)
parabolic cylinder functions Dv(z)
parabolic cylinder functions Vv(x)
parabolic cylinder functions W(a,+/-x)
characteristic values for the Mathieu and modified Mathieu functions.
expansion coefficients for the Mathieu and modified Mathieu functions.
Mathieu functions
modified Mathieu functions of the first and second kinds
characteristic values for spheroidal wave functions.
angular spheroidal wave functions
error function.
Fresnel Integrals.
modified Fresnel integrals.
complex zeros of the error function.
complex zeros of the Fresnel Integrals.
cosine and sine integrals
complete and incomplete elliptic integrals of the first and second kinds.
complete and incomplete elliptic integrals of the third kind.
Jacobian elliptic functions.
exponential integral E1(x)
exponential integrals En(x)
exponential integral Ei(x)

### Cite As

Ben Barrowes (2022). Computation of Special Functions (https://www.mathworks.com/matlabcentral/fileexchange/6218-computation-of-special-functions), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R14SP1
Compatible with any release
##### Platform Compatibility
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