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Research paper | Publishing Language: Chinese

On Algebraic Differential Equations Concerning the Euler Gamma Function Γ and a Class of L-Functions

Xiaomin Li, Yixuan Li
School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China
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Abstract

This paper studies the algebraic independence of Euler gamma function Γ and any one of a class S ~ of L-functions satisfying the axioms (Ⅰ)—(Ⅴ), and proves that the Euler gamma function Γ and any one of a class S ~ of L-functions do not satisfy any given non-trivial algebraic differential equation. The main result of this paper improves and extends the corresponding results by Li and Ye in 2016 and by Chen and Wang in 2021 respectively.

Keywords

Euler gamma function Γa class S of L-functionsdifferential independencealgebraic differential equation
CLC number: O174.52 Document code: A Article ID: 1672-5174(2025)07Ⅱ-106-05

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Periodical of Ocean University of China
Volume 55 Issue S1,
July 2025
Pages 106-109
DOI: 10.16441/j.cnki.hdxb.20220036

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Cite this article:
Li X, Li Y. On Algebraic Differential Equations Concerning the Euler Gamma Function Γ and a Class of L-Functions. Periodical of Ocean University of China, 2025, 55(S1): 106-109. https://doi.org/10.16441/j.cnki.hdxb.20220036

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Received: 13 January 2023
Revised: 04 April 2023
Published: 01 July 2025
© Periodical of Ocean University of China