If the first parameter is a non-negative integer, the JacobiP(n, a, b, x) function computes the nth Jacobi polynomial with parameters a and b evaluated at x.

These polynomials are orthogonal on the interval  with respect to the weight function  when a and b are greater than -1. They satisfy the following:

The Jacobi polynomials are undefined for negative integer values of a or b.

The polynomials satisfy the following recurrence relation:

For n not equal to a non-negative integer, the analytic extension of the Jacobi polynomial is given by the following: