Title

A Proof Of New Summation Formulas By Using Sampling Theorems

Authors

Authors

A. I. Zayed

Comments

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Abbreviated Journal Title

Proc. Amer. Math. Soc.

Keywords

TRIGONOMETRIC SERIES; BESSEL FUNCTIONS; HYPERGEOMETRIC FUNCTIONS; SHANNON AND KRAMER SAMPLING THEOREMS; STURM-LIOUVILLE PROBLEMS; LAGRANGE INTERPOLATION; Mathematics, Applied; Mathematics

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.

Journal Title

Proceedings of the American Mathematical Society

Volume

117

Issue/Number

3

Publication Date

1-1-1993

Document Type

Article

DOI Link

http://dx.doi.org/10.2307/2159131

Language

English

First Page

699

Last Page

710

WOS Identifier

WOS:A1993KM07300018

ISSN

0002-9939

Recommended Citation

"A Proof Of New Summation Formulas By Using Sampling Theorems" (1993). Faculty Bibliography 1990s. 968.
https://stars.library.ucf.edu/facultybib1990/968