# polpak

polpak, a MATLAB code which evaluates a variety of mathematical functions.

It includes routines to evaluate the recursively defined polynomial families of

• Bernoulli
• Bernstein
• Cardan
• Charlier
• Chebyshev
• Euler
• Gegenbauer
• Hermite
• Jacobi
• Krawtchouk
• Laguerre
• Legendre
• Meixner
• Zernike
A variety of other polynomials and functions have been added. In a few cases, the new recursive feature of FORTRAN90 has been used (but NOT for the factorial function!)

### Languages:

polpak is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and an Octave version and a Python version

### Related Data and Programs:

bernstein_polynomial, a MATLAB code which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

chebyshev_polynomial, a MATLAB code which evaluates the Chebyshev polynomial and associated functions.

clausen, a MATLAB code which evaluates a Chebyshev approximant to the Clausen function Cl2(x).

cordic, a MATLAB code which use the CORDIC method to compute certain elementary functions.

fn, a MATLAB code which approximates elementary and special functions using Chebyshev polynomials, by Wayne Fullerton.

hermite_polynomial, a MATLAB code which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.

jacobi_polynomial, a MATLAB code which evaluates the Jacobi polynomial and associated functions.

laguerre_polynomial, a MATLAB code which evaluates the Laguerre polynomial, the generalized Laguerre polynomial, and the Laguerre function.

legendre_polynomial, a MATLAB code which evaluates the Legendre polynomial and associated functions.

legendre_product_polynomial, a MATLAB code which defines Legendre product polynomials, creating a multivariate polynomial as the product of univariate Legendre polynomials.

lobatto_polynomial, a MATLAB code which evaluates Lobatto polynomials, similar to Legendre polynomials except that they are zero at both endpoints.

spherical_harmonic, a MATLAB code which evaluates spherical harmonic functions.

test_values, a MATLAB code which contains some sample values of many mathematical functions.

### Source Code:

Last revised on 09 May 2021.