Some generalizations of Carlitz’s theorem

H. M. (Hari Mohan) Srivastava

Vol. 85 (1979), No. 2, 471–477

DOI: 10.2140/pjm.1979.85.471

Abstract

Recently, L. Carlitz extended certain known generating functions for Laguerre and Jacobi polynomials to the forms:

respectively, where c_n^(α) and d_n^(α,β) are general one- and two-parameter coefficients. In the present paper some generalizations of Carlitz’s results of this kind are derived, and a number of interesting applications of the main theorem are given.

Mathematical Subject Classification 2000

Primary: 33A65, 33A65

Secondary: 05A15

Milestones

Received: 25 April 1979

Published: 1 December 1979