A proof of new summation formulae by using sampling theorems
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- by Ahmed I. Zayed PDF
- Proc. Amer. Math. Soc. 117 (1993), 699-710 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 699-710
- MSC: Primary 40A25; Secondary 34L10, 42C15, 94A24
- DOI: https://doi.org/10.1090/S0002-9939-1993-1116276-8
- MathSciNet review: 1116276