Shifted Legendre Polynomials

**LEGENDRE_SHIFTED_POLYNOMIAL**,
a C 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)

The computer code and data files described and made available on this web page are distributed under the GNU LGPL 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 library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

CHEBYSHEV_POLYNOMIAL, a C 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 C library which evaluates the Gegenbauer polynomial and associated functions.

HERMITE_POLYNOMIAL, a C library which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.

JACOBI_POLYNOMIAL, a C library which evaluates the Jacobi polynomial and associated functions.

LAGUERRE_POLYNOMIAL, a C library which evaluates the Laguerre polynomial, the generalized Laguerre polynomial, and the Laguerre function.

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

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

legendre_shifted_polynomial_test

LOBATTO_POLYNOMIAL, a C library which evaluates Lobatto polynomials, similar to Legendre polynomials except that they are zero at both endpoints.

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

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

- legendre_shifted_polynomial.c, the source code.
- legendre_shifted_polynomial.sh, compiles the source code.
- legendre_shifted_polynomial.h, the include file.