legendre_shifted_polynomial

legendre_shifted_polynomial, an Octave code 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 MIT license

Languages:

legendre_shifted_polynomial is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

legendre_shifted_polynomial_test

legendre_rule, an Octave code which computes a 1D Gauss-Legendre quadrature rule.

octave_polynomial, an Octave code which analyzes a variety of polynomial families, returning the polynomial values, coefficients, derivatives, integrals, roots, or other information.

polpak, an Octave code which evaluates a variety of mathematical functions.

test_values, an Octave code which supplies test values of various mathematical functions.

Source Code:

• 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