**legendre_polynomial**,
a Python code which
evaluates the Legendre polynomial and associated functions.

The Legendre polynomial P(n,x) can be defined by:

P(0,x) = 1 P(1,x) = x P(n,x) = (2*n-1)/n * x * P(n-1,x) - (n-1)/n * P(n-2,x)where n is a nonnegative integer.

The N zeroes of P(n,x) are the abscissas used for Gauss-Legendre quadrature of the integral of a function F(X) with weight function 1 over the interval [-1,1].

The Legendre polynomials are orthogonal under the inner product defined as integration from -1 to 1:

Integral ( -1 <= x <= 1 ) P(i,x) * P(j,x) dx = 0 if i =/= j = 2 / ( 2*i+1 ) if i = j.

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

**legendre_polynomial** is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version and
a Python version.

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- legendre_polynomial.py, the source code.
- legendre_polynomial.sh, runs all the tests.
- legendre_polynomial.txt, the output file.