A short note on a extended finite secant series

Robert Reynolds; Robert Reynolds

doi:10.3934/math.20231376

AIMS Mathematics

2023, Volume 8, Issue 11: 26882-26895. doi: 10.3934/math.20231376

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A short note on a extended finite secant series

Robert Reynolds ^,

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

Received: 11 July 2023 Revised: 01 September 2023 Accepted: 13 September 2023 Published: 21 September 2023
MSC : 30E20, 33-01, 33-03, 33-04

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.
- Hurwitz-Lerch zeta function,
- secant function,
- gamma function
Citation: Robert Reynolds. A short note on a extended finite secant series[J]. AIMS Mathematics, 2023, 8(11): 26882-26895. doi: 10.3934/math.20231376

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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.

References

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