Ultraspherical Polynomial
(or Gegenbauer polynomial). Ultraspherical polynomials are a special family of polynomials of successively increasing degree. For n = 0,1, 2,. . ., the ultraspherical polynomials 
of degree n are the coefficients of an in the power series expansion of the function
Ultraspherical polynomials are orthogonal on the interval [–1, + 1] with respect to the weight function (1 – x2)λ–(½). Ultra spherical polynomials constitute a special case of Jacobi polynomials.
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