LEGENDRE_SHIFTED_POLYNOMIAL Shifted Legendre Polynomials

LEGENDRE_SHIFTED_POLYNOMIAL is a Python library 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)

Languages:

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.

Related Data and Programs:

BERNSTEIN_POLYNOMIAL, a Python library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

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.

GEGENBAUER_POLYNOMIAL, a Python library which evaluates the Gegenbauer polynomial and associated functions.

LEGENDRE_POLYNOMIAL, a Python library which evaluates the Legendre polynomials and associated functions;

LEGENDRE_PRODUCT_POLYNOMIAL, a Python library which defines Legendre product polynomials, creating a multivariate polynomial as the product of univariate Legendre polynomials.

POLPAK, a Python library which evaluates a variety of mathematical functions.

TEST_VALUES, a Python library which supplies test values of various mathematical functions.

Source Code:

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

Last revised on 15 March 2016.