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Research Article | Open Access

A short note on a extended finite secant series

Department of Mathematics and Statitics, York University, 4700 Keele Street, Ross Building, N520, Ontario, M3J 1P3, Canada
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Abstract

In this paper, a summation formula for a general family of a finite secant sum has been extended by making use of a particularly convenient integration contour method. The main theorem derived from this approach is the finite sum involving the Hurwitz-Lerch zeta function. This theorem for particular values is used to derive the finite product of the fifth roots of the quotient product of the gamma function along with finite sums and functional equations involving trigonometric functions.

Keywords

Hurwitz-Lerch zeta functionsecant functiongamma function
CLC number: 30E20, 33-01, 33-03, 33-04

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AIMS Mathematics
Volume 8 Issue 11,
November 2023
Pages 26882-26895
DOI: 10.3934/math.20231376

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Cite this article:
Reynolds R. A short note on a extended finite secant series. AIMS Mathematics, 2023, 8(11): 26882-26895. https://doi.org/10.3934/math.20231376

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Received: 11 July 2023
Revised: 01 September 2023
Accepted: 13 September 2023
Published: 15 November 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)