legendre_shifted_polynomial, a C 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 C code which evaluates the Bernstein polynomials, useful for uniform approximation of functions;
CHEBYSHEV_POLYNOMIAL, a C 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 C code which evaluates the Gegenbauer polynomial and associated functions.
HERMITE_POLYNOMIAL, a C code which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.
JACOBI_POLYNOMIAL, a C code which evaluates the Jacobi polynomial and associated functions.
LAGUERRE_POLYNOMIAL, a C code which evaluates the Laguerre polynomial, the generalized Laguerre polynomial, and the Laguerre function.
LEGENDRE_POLYNOMIAL, a C code which evaluates the Legendre polynomials and associated functions;
LEGENDRE_PRODUCT_POLYNOMIAL, a C code which defines Legendre product polynomials, creating a multivariate polynomial as the product of univariate Legendre polynomials.
legendre_shifted_polynomial_test
LOBATTO_POLYNOMIAL, a C code which evaluates Lobatto polynomials, similar to Legendre polynomials except that they are zero at both endpoints.
POLPAK, a C code which evaluates a variety of mathematical functions.
TEST_VALUES, a C code which supplies test values of various mathematical functions.