Startseite Monotonicity of the ratio of two arbitrary gaussian hypergeometric functions
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Monotonicity of the ratio of two arbitrary gaussian hypergeometric functions

  • Zhong-Xuan Mao und Jing-Feng Tian EMAIL logo
Veröffentlicht/Copyright: 9. August 2025
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Abstract

The Gaussian hypergeometric function is an important class of special functions, whose mathematical properties have long been of interest to the academic community. In this paper, by utilizing monotonicity rules, we establish the necessary and sufficient conditions for the monotonicity of the ratio of two Gaussian hypergeometric functions xFa1,b1;c1;xFa2,b2;c2;x for positive parameters ai, bi, ci (i = 1, 2). Subsequently, we also derive some corollaries and provide some conclusions related to the complete elliptic integral function and its variants.

  1. (Communicated by Marek Balcerzak)

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Received: 2024-09-11
Accepted: 2025-04-02
Published Online: 2025-08-09
Published in Print: 2025-08-26

© 2025 Mathematical Institute Slovak Academy of Sciences

Heruntergeladen am 23.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2025-0060/html
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