The special case of [beta] = [alpha] of the Jacobi polynomial is called Ultraspherical polynomial and is denoted by [P.
n](x) of the first and second kinds respectievely are special Ultraspherical polynomials.
Balazs  investigated the above problem on the interval [-1,1], when the nodes are the zeros of the ultraspherical polynomial [P.
BALAZS, Weighted (0, 2) -interpolation on the zeros of the ultraspherical polynomials, (in Hungarian: Sulyozott (0, 2)-interpolacio ultraszferikus polinom gyokein), MTA IILoszt.
In  Olver and Townsend presented a fast spectral method for solving linear differential equations using bases of ultraspherical polynomials
, which has subsequently been exploited in Chebfun  and ApproxFun .
LORCH, Inequalities for ultraspherical polynomials
and the gamma function, J.
ISMAIL, A generalization of ultraspherical polynomials
, in Studies in Pure Mathematics, P.
14] --, Zeros of ultraspherical polynomials
and the Hilbert-Klein formulas, J.
uncertainty principle, self-adjoint operators, symmetric operators, normal operators, periodic functions, ultraspherical polynomials, sphere.
Ultraspherical polynomials are solutions of the differential equations [L.