Double Gegenbauer expansion of $|s-t{|}^{\alpha }$

Abstract

We give a Gegenbauer expansion of the two variable function $|s-t{|}^{\alpha }$ in terms of the ultraspherical polynomials $C_l^{\lambda }(s)$ and $C_m^{\mu }(t)$. Generalization, specialization, and limits of the expansion are also discussed.

16 pages, to appear in Integral Transforms and Special Functions

References in corpus (2)

• Generalized Bernstein--Reznikov integrals
• The sl_3 Selberg integral