Derivation and Evaluations of a Generalized Finite Integral Involving Transcendental and Hypergeometric Kernels

Robert Reynolds

doi:10.33401/fujma.1814870

Derivation and Evaluations of a Generalized Finite Integral Involving Transcendental and Hypergeometric Kernels

Abstract

In this paper we have established a finite integral involving the product of the hypergeometric, exponential, and rational functions in terms of an infinite series. The infinite series involves the product of the incomplete gamma function and a rational function which can be reduced to the Hurwitz-Lerch zeta function as a special case. Other results are possible for various special cases of the parameters involved. The finite integral will be used to derive formulae involving elliptic functions, product of logarithm functions and a few other special case examples which are new to best of our knowledge along with errata for examples in some well known textbooks. The method used to derive this integral is contour integration. The parameters involved are valid over the complex plane unless stated otherwise.

Keywords

References

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Details

Primary Language

English

Subjects

Mathematical Methods and Special Functions

Journal Section

Research Article

Authors

Robert Reynolds ^*
0000-0002-4230-9925
Canada

Publication Date

June 30, 2026

Submission Date

October 31, 2025

Acceptance Date

June 23, 2026

Published in Issue

Year 2026 Volume: 9 Number: 2

DOI

https://doi.org/10.33401/fujma.1814870

IZ

https://izlik.org/JA37RH36RL

Cite

RIS / Bibtex

APA

Reynolds, R. (2026). Derivation and Evaluations of a Generalized Finite Integral Involving Transcendental and Hypergeometric Kernels. Fundamental Journal of Mathematics and Applications, 9(2), 92-101. https://doi.org/10.33401/fujma.1814870

AMA

1.Reynolds R. Derivation and Evaluations of a Generalized Finite Integral Involving Transcendental and Hypergeometric Kernels. Fundam. J. Math. Appl. 2026;9(2):92-101. doi:10.33401/fujma.1814870

Chicago

Reynolds, Robert. 2026. “Derivation and Evaluations of a Generalized Finite Integral Involving Transcendental and Hypergeometric Kernels”. Fundamental Journal of Mathematics and Applications 9 (2): 92-101. https://doi.org/10.33401/fujma.1814870.

EndNote

Reynolds R (June 1, 2026) Derivation and Evaluations of a Generalized Finite Integral Involving Transcendental and Hypergeometric Kernels. Fundamental Journal of Mathematics and Applications 9 2 92–101.

IEEE

[1]R. Reynolds, “Derivation and Evaluations of a Generalized Finite Integral Involving Transcendental and Hypergeometric Kernels”, Fundam. J. Math. Appl., vol. 9, no. 2, pp. 92–101, June 2026, doi: 10.33401/fujma.1814870.

ISNAD

Reynolds, Robert. “Derivation and Evaluations of a Generalized Finite Integral Involving Transcendental and Hypergeometric Kernels”. Fundamental Journal of Mathematics and Applications 9/2 (June 1, 2026): 92-101. https://doi.org/10.33401/fujma.1814870.

JAMA

1.Reynolds R. Derivation and Evaluations of a Generalized Finite Integral Involving Transcendental and Hypergeometric Kernels. Fundam. J. Math. Appl. 2026;9:92–101.

MLA

Reynolds, Robert. “Derivation and Evaluations of a Generalized Finite Integral Involving Transcendental and Hypergeometric Kernels”. Fundamental Journal of Mathematics and Applications, vol. 9, no. 2, June 2026, pp. 92-101, doi:10.33401/fujma.1814870.

Vancouver

1.Robert Reynolds. Derivation and Evaluations of a Generalized Finite Integral Involving Transcendental and Hypergeometric Kernels. Fundam. J. Math. Appl. 2026 Jun. 1;9(2):92-101. doi:10.33401/fujma.1814870