Extended Moreno-García cosine products

Robert Reynolds; Robert Reynolds

doi:10.3934/math.2023157

AIMS Mathematics

2023, Volume 8, Issue 2: 3049-3063. doi: 10.3934/math.2023157

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Research article

Extended Moreno-García cosine products

Robert Reynolds ^,

Department of Mathematics and Statistics, York University, Toronto, ON, M3J1P3, Canada

Received: 16 August 2022 Revised: 18 October 2022 Accepted: 24 October 2022 Published: 15 November 2022
MSC : Primary 30E20, 33-01, 33-03, 33-04

The Moreno-García cosine product is extended to evaluate an extensive number of trigonometric products previously published. The products are taken over finite and infinite domains defined in terms of the Hurwitz-Lerch Zeta function, which can be simplified to composite functions in special cases of integer values of the parameters involved. The results obtained include generalizations of finite and infinite products cosine functions, in certain cases raised to a complex number power.
- cosine function,
- Hurwitz-Lerch Zeta function,
- Cauchy integral,
- infinite product,
- finite product,
- golden ratio
Citation: Robert Reynolds. Extended Moreno-García cosine products[J]. AIMS Mathematics, 2023, 8(2): 3049-3063. doi: 10.3934/math.2023157

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Abstract

The Moreno-García cosine product is extended to evaluate an extensive number of trigonometric products previously published. The products are taken over finite and infinite domains defined in terms of the Hurwitz-Lerch Zeta function, which can be simplified to composite functions in special cases of integer values of the parameters involved. The results obtained include generalizations of finite and infinite products cosine functions, in certain cases raised to a complex number power.

References

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