Recursive Polynomials

POLPAK, a MATLAB library which evaluates a variety of mathematical functions.

It includes routines to evaluate the recursively defined polynomial families of

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!)


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


POLPAK is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version

Related Data and Programs:

BERNSTEIN_POLYNOMIAL, a MATLAB library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

CHEBYSHEV_POLYNOMIAL, a MATLAB library which evaluates the Chebyshev polynomial and associated functions.

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

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

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

GSL, a C++ library which evaluates many special functions.

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

JACOBI_POLYNOMIAL, a MATLAB library which evaluates the Jacobi polynomial and associated functions.

LAGUERRE_POLYNOMIAL, a MATLAB library which evaluates the Laguerre polynomial, the generalized Laguerre polynomial, and the Laguerre function.

LEGENDRE_POLYNOMIAL, a MATLAB library which evaluates the Legendre polynomial and associated functions.

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

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


SPHERICAL_HARMONIC, a MATLAB library which evaluates spherical harmonic functions.

TEST_VALUES, a MATLAB library which contains some sample values of many mathematical functions.

Source Code:

Last revised on 25 February 2019.