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.

Related Data and Programs:

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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.

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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.

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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.

Source Code:

Examples and Tests:

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Last revised on 14 March 2016.