Lie theory and Humbert function $ \Psi_{1} $

Mohamed M. Awad; Nada Mostafa; Ayman Shehata; Mohamed M. Awad; Nada Mostafa; Ayman Shehata

doi:10.3934/math.2026240

AIMS Mathematics

2026, Volume 11, Issue 3: 5824-5840. doi: 10.3934/math.2026240

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Research article

Lie theory and Humbert function $ \Psi_{1} $

1.
Department of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Suez Canal University, El-Sheik Zayed 41522, Ismailia, Egypt
3.
Department of Mathematics and Computer, Faculty of Science, New Valley University, El-khargah 72511, Egypt; nadamoustafa@sci.nvu.edu.eg
4.
Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt; aymanshehata@science.aun.edu.eg

Received: 14 December 2025 Revised: 29 January 2026 Accepted: 04 February 2026 Published: 09 March 2026
MSC : 16W25, 17B40, 22E30, 33C80, 70G65, 76M60

The paper is devoted to bringing hypergeometric functions (HFs) within the purview of Lie theory by constructing a dynamical symmetry algebra of Humbert function $ \Psi_{1} $. Multiplier representation theory of Lie groups and algebras is then used to obtain a generating function for basic analogue of Humbert function $ \Psi_{1} $.
- Lie theory,
- Lie algebra method,
- dynamical symmetry algebra,
- Weisner's group theoretic method,
- Humbert function $ \Psi_{1} $,
- group theoretical analysis
Citation: Mohamed M. Awad, Nada Mostafa, Ayman Shehata. Lie theory and Humbert function $ \Psi_{1} $[J]. AIMS Mathematics, 2026, 11(3): 5824-5840. doi: 10.3934/math.2026240

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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 $ \Psi_{1} $. Multiplier representation theory of Lie groups and algebras is then used to obtain a generating function for basic analogue of Humbert function $ \Psi_{1} $.

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