LEGENDRE_SHIFTED_POLYNOMIAL
Shifted Legendre Polynomials

LEGENDRE_SHIFTED_POLYNOMIAL is a FORTRAN90 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)
      

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

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 FORTRAN90 library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

CHEBYSHEV_POLYNOMIAL, a FORTRAN90 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 FORTRAN90 library which evaluates the Gegenbauer polynomial and associated functions.

HERMITE_POLYNOMIAL, a FORTRAN90 library which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.

JACOBI_POLYNOMIAL, a FORTRAN90 library which evaluates the Jacobi polynomial and associated functions.

LAGUERRE_POLYNOMIAL, a FORTRAN90 library which evaluates the Laguerre polynomial, the generalized Laguerre polynomial, and the Laguerre function.

LEGENDRE_POLYNOMIAL, a FORTRAN90 library which evaluates the Legendre polynomials and associated functions;

LEGENDRE_PRODUCT_POLYNOMIAL, a FORTRAN90 library which defines Legendre product polynomials, creating a multivariate polynomial as the product of univariate Legendre polynomials.

LOBATTO_POLYNOMIAL, a FORTRAN90 library which evaluates Lobatto polynomials, similar to Legendre polynomials except that they are zero at both endpoints.

POLPAK, a FORTRAN90 library which evaluates a variety of mathematical functions.

TEST_VALUES, a FORTRAN90 library which supplies test values of various mathematical functions.

Source Code:

• legendre_shifted_polynomial.f90, the source code.

Examples and Tests:

• legendre_shifted_polynomial_test.f90, a sample calling program.
• legendre_shifted_polynomial_test.txt, the output file.

List of Routines:

• P01_POLYNOMIAL_VALUE evaluates the shifted Legendre polynomials P01(n,x).
• P01_POLYNOMIAL_VALUES: the shifted Legendre polynomials.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.