International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 707-717
doi:10.1155/S0161171285000795

A representation of Jacobi functions

E.Y. Deeba1 and E.L. Koh2

1Department of Applied Mathematical Sciences, University of Houston-Downtown, Houston 77002, Texas, USA
 2Department of Mathematics \& Statistics, University of Regina, Regina S45 0A2, Canada

Abstract

Recently, the continuous Jacobi transform and its inverse are defined and studied in [1] and [2]. In the present work, the transform is used to derive a series representation for the Jacobi functions Pλ(α,β)(x), −½≤α, β≤½, α+β=0, and λ≥−½. The case α=β=0 yields a representation for the Legendre functions and has been dealt with in [3]. When λ is a positive integer n, the representation reduces to a single term, viz., the Jacobi polynomial of degree n.