legendre_shifted_polynomial, a Python code which evaluates the shifted Legendre polynomial.
The standard Legendre polynomial P(n,x) is defined over the interval [-1,+1]. The shifted Legendre polynomial P01(n,x) is shifted to the interval [0,1]. The relationships are:
P01(n,x) = P(n,(x+1)/2)
P(n,x) = P01(n,2*x-1)
The computer code and data files described and made available on this web page are distributed under the MIT license
legendre_shifted_polynomial is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.
bernstein_polynomial, a python code which evaluates the bernstein polynomials, useful for uniform approximation of functions;
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.
gegenbauer_polynomial, a python code which evaluates the gegenbauer polynomial and associated functions.
legendre_polynomial, a python code which evaluates the legendre polynomials and associated functions;
legendre_product_polynomial, a python code which defines legendre product polynomials, creating a multivariate polynomial as the product of univariate legendre polynomials.
polpak, a python code which evaluates a variety of mathematical functions.
test_values, a python code which supplies test values of various mathematical functions.