If the first parameter is a non-negative integer, then the ChebyshevU(n, x) function computes the nth Chebyshev polynomial of the second kind evaluated at x.

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

Chebyshev polynomials of the second kind satisfy the following recurrence relation:

where ChebyshevU(0,x) = 1 and ChebyshevU(1,x) = 2*x.

This definition is analytically extended for arbitrary values of the first argument by