Gauss超几何函数关于参数的单调性
Monotonicity Properties of Gaussian Hypergeometric Functions with Respect to the Parameter
DOI: 10.12677/PM.2023.1312387, PDF,   
作者: 温佳乐, 马晓艳*：浙江理工大学理学院，浙江 杭州
关键词: Gauss超几何函数；单调性；参数；Gaussian Hypergeometric Function； Monotonicity； Parameter
摘要: 本文给出了Gauss超几何函数F(a,c−a;c;x)和F(a−1,c−a;c;x)与初等函数组合函数的一类新的形式，研究这类形式下的组合函数关于参数a的单调性质。本文借助函数的级数展开表达式以及Psi函数、Gamma函数的递推公式，利用对数求导法给出了这类组合函数关于参数a的单调性的充分必要条件。
Abstract: This paper gives a new form of the combination of Gaussian hypergeometric functions F(a,c−a;c;x), F(a−1,c−a;c;x) and elementary functions, and studies the monotonicity of the new-form combination function with respect to the parameter a. This paper uses the series ex-pansion expression of functions and the recurrence formulas of Psi and Gamma functions，as well as the logarithmic differentiation method to provide necessary and sufficient conditions for the monotonicity of the combination function with respect to the parameter a.
文章引用：温佳乐, 马晓艳. Gauss超几何函数关于参数的单调性[J]. 理论数学, 2023, 13(12): 3742-3748. https://doi.org/10.12677/PM.2023.1312387

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