Vol. 85, No. 2, 1979

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ISSN: 0030-8730
Some generalizations of Carlitz’s theorem

H. M. (Hari Mohan) Srivastava

Vol. 85 (1979), No. 2, 471–477
Abstract

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

∑∞  (α+λn)tn-       ∞∑   (α+ λn,β+μn)tn-
cn     n! and      dn         n!,
n=0                n=0

respectively, where cn(α) and dn(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
Authors
H. M. (Hari Mohan) Srivastava