Shifted Legendre Polynomials

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

CHEBYSHEV_POLYNOMIAL, a Python 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_POLYNOMIAL, a Python library which evaluates the Legendre polynomials and associated functions;

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

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

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

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