Chebyshev Polynomials of the Second Kind

We construct the family of Chebyshev polynomials of the second kind. This collection of polynomials is again an orthogonal family with respect to the measure (1-x^2)^{1/2} dx, so they arise in the study of spherical harmonics and questions of angular momentum. We show that this family is orthogonal and prove that there is a recursion for members of this family. Chebyshev polynomials of the first kind are studied here: • Chebyshev Polynomials
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