Infinite sum of products of continuous $q$-ultraspherical functions

Abstract

Let C n (x; ß\q) be the continuous g-ultra-spherical polynomial and D n {x\ß\q) be the g-ultraspherical function of the second kind.By exploiting a special case of the recently found g-Feldheim bilinear sum, the following infinite sums are computed: / \ 2 £ ((^jt) ^Yzfß n/2 Cn(x;ß\g)C n (y,ß\g)C n (z;ß\g), n=0 0 < ß < 1, 0 < q < 1, and Z -'(P ,<2)n 1-P 71 = 0 0< q < ß < 1. 1. Introduction.Recently, Rahman [8] showed that O<0<7T and (1.2) (l+/?)W<Z)n V -Q»(e-^/?*,(/9g)*,-/9*,-(/?9)*)),O<0<ir,

Locations

• Rocky Mountain Journal of Mathematics - View - PDF