**polpak**,
a Python code which
evaluates a variety of mathematical functions, polynomials, and
sequences, including Bell, Benford, Bernoulli, Bernstein, Cardan,
Catalan, Charlier, Chebyshev, Collatz, Delannoy, Euler, Fibonacci,
Gegenbauer, Gudermannian, Harmonic, Hermite, Hofstadter, Jacobi,
Krawtchouk, Laguerre, Lambert, Legendre, Lerch, Meixner, Mertens,
Moebius, Motzkin, Phi, Stirling, Tau, Tribonacci, Zernike.

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
an Octave version and
a Python version

asa103, a Python code which evaluates the digamma or psi function, by Jose Bernardo. This is a version of Applied Statistics Algorithm 103.

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

collatz_dict, a Python code which demonstrates how the Python dict variable type can be used to efficiently record data about the Collatz iteration.

fn, a Python code 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 code which evaluates the Legendre polynomial and associated functions.

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

- polpak.py, the source code;
- polpak.sh, runs all the tests;
- polpak.txt, the output file;