The G(n, a, x) function computes the nth ultraspherical (Gegenbauer) polynomial with parameter a evaluated at x.

These polynomials are orthogonal on the interval  with respect to the weight function . For  they satisfy:

When , , and  for , where  is the nth Chebyshev polynomial of the first kind.

The ultraspherical polynomials satisfy the following recurrence relation, for .