Shifted Legendre Polynomials

**LEGENDRE_SHIFTED_POLYNOMIAL**
is a MATLAB 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 MATLAB library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

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

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

INT_EXACTNESS_LEGENDRE, a MATLAB program which tests the polynomial exactness of Gauss-Legendre quadrature rules.

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

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

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

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

LEGENDRE_RULE, a MATLAB program which computes a 1D Gauss-Legendre quadrature rule.

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

PCE_LEGENDRE, a MATLAB program which assembles the system matrix of a 2D stochastic PDE, using a polynomal chaos expansion in terms of Legendre polynomials;

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

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

- p_polynomial_value.m, evaluates the Legendre polynomials P(n,x).
- p_polynomial_value_test.m
- p_polynomial_values.m, returns values of the Legendre polynomials P(n,x).
- p_polynomial_values_test.m
- timestamp.m, prints the current YMDHMS date as a time stamp.

- legendre_shifted_polynomial_test.m, calls all the tests.
- legendre_shifted_polynomial_test_output.txt, the output file.

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