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Research Article | Open Access

Lie theory and Humbert function Ψ 1

Department of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Department of Mathematics, Faculty of Science, Suez Canal University, El-Sheik Zayed 41522, Ismailia, Egypt
Department of Mathematics and Computer, Faculty of Science, New Valley University, El-khargah 72511, Egypt; nadamoustafa@sci.nvu.edu.eg
Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt; aymanshehata@science.aun.edu.eg
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Abstract

The paper is devoted to bringing hypergeometric functions (HFs) within the purview of Lie theory by constructing a dynamical symmetry algebra of Humbert function Ψ 1 . Multiplier representation theory of Lie groups and algebras is then used to obtain a generating function for basic analogue of Humbert function Ψ 1 .

Keywords

Lie theoryLie algebra methoddynamical symmetry algebraWeisner's group theoretic methodHumbert function Ψ1group theoretical analysis
CLC number: 16W25, 17B40, 22E30, 33C80, 70G65, 76M60

References

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AIMS Mathematics
Volume 11 Issue 3,
March 2026
Pages 5824-5840
DOI: 10.3934/math.2026240

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Cite this article:
Awad MM, Mostafa N, Shehata A. Lie theory and Humbert function Ψ 1 . AIMS Mathematics, 2026, 11(3): 5824-5840. https://doi.org/10.3934/math.2026240

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Received: 14 December 2025
Revised: 29 January 2026
Accepted: 04 February 2026
Published: 15 March 2026
©2026 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)