jacobi_polynomial, a MATLAB code 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 FORTRAN90 version and a MATLAB version.
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