# POLPAK Recursive Polynomials

POLPAK is a Python library 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 a Python version

### Related Data and Programs:

ASA103, a Python library which evaluates the digamma or psi function, by Jose Bernardo. This is a version of Applied Statistics Algorithm 103.

CHEBYSHEV_POLYNOMIAL, a Python library which considers the Chebyshev polynomials T(i,x), U(i,x), V(i,x) and W(i,x). Functions are provided to evaluate the polynomials, determine their zeros, produce their polynomial coefficients, produce related quadrature rules, project other functions onto these polynomial bases, and integrate double and triple products of the polynomials.

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

FN, a Python library which approximates elementary and special functions using Chebyshev polynomials; functions include Airy, Bessel I, Bessel J, Bessel K, Bessel Y, beta, confluent hypergeometric, cosine integral, Dawson's integral, digamma (psi), error, exponential integral, gamma, hyperbolic cosine integral, hyperbolic sine integral, incomplete gamma, log gamma, logarithmic integral, Pochhammer, psi, sine integral, Spence; by Wayne Fullerton.

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

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

### Examples and Tests:

You can go up one level to the Python source codes.

Last revised on 19 June 2018.