Title

A Proof Of New Summation Formulae By Using Sampling Theorems

Keywords

Bessel functions; Hypergeometric functions; Shannon and kramer sampling theorems; Trigonometric series

Abstract

Using symbolic manipulation programs, William Gosper has obtained in the last two years new, but unusual, summation formulae involving trigonometric functions. Recently, Ismail and Zhang have been able to prove mathematically some of these formulae and generalize them to summation formulae involving the Bessel functions of the first kind. In this paper we show that some of Gosper’s formulae, as well as their generalization by Ismail and Zhang, can be obtained from already known results in sampling theory. Moreover, we show that sampling theory can actually produce other new summation formulae, involving different kinds of special functions, in a straightforward fashion. © 1993 American Mathematical Society.

Publication Date

1-1-1993

Publication Title

Proceedings of the American Mathematical Society

Volume

117

Issue

3

Number of Pages

699-710

Document Type

Article

Identifier

scopus

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/S0002-9939-1993-1116276-8

Socpus ID

35348989631 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/35348989631

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