A Proof Of New Summation Formulas By Using Sampling Theorems

    Authors

    A. I. Zayed

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    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

    Language

    English

    First Page

    699

    Last Page

    710

    WOS Identifier

    WOS:A1993KM07300018

    ISSN

    0002-9939

    Share

    COinS