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 MIT 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.
