JACOBI_POLYNOMIAL is a MATLAB library which evaluates the Jacobi polynomial.
For a given choice of the parameters a and b, both greater than -1, the Jacobi polynomials are a set of polynomials which are pairwise orthogonal with respect to the integral:
integral (-1<=x<=+1) J(i,a,b,x) J(j,a,b,x) (1-x)^a (1+x)^b dxThat is, this integral is 0 unless i = j. J(i,a,b,x) indicates the Jacobi polynomial of degree i.
The standard Jacobi polynomials can be defined by a three term recurrence formula that is a bit too ugly to quote here.
It is worth noting that the definition of the Jacobi polynomials is general enough that it includes some familiar families as special cases:
The computer code and data files made available on this web page are distributed under the GNU LGPL license.
JACOBI_POLYNOMIAL is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.
BERNSTEIN_POLYNOMIAL, a MATLAB library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;
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HERMITE_POLYNOMIAL, a MATLAB library which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.
JACOBI_RULE, a MATLAB program which can compute and print a Gauss-Jacobi quadrature rule.
LAGUERRE_POLYNOMIAL, a MATLAB library which evaluates the Laguerre polynomial, the generalized Laguerre polynomials, and the Laguerre function.
LEGENDRE_POLYNOMIAL, a MATLAB library which evaluates the Legendre polynomial and associated functions.
LOBATTO_POLYNOMIAL, a MATLAB library which evaluates Lobatto polynomials, similar to Legendre polynomials except that they are zero at both endpoints.
POLPAK, a MATLAB library which evaluates a variety of mathematical functions.
TEST_VALUES, a MATLAB library which supplies test values of various mathematical functions.
You can go up one level to the MATLAB source codes.