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An integral representation of the Gauss hypergeometric functions and its applications

Veröffentlicht/Copyright: 28. Oktober 2025
Analysis
Aus der Zeitschrift Analysis

Abstract

In the work, the author derives an integral representation of the Gauss hypergeometric functions F 1 2 ( a - 1 2 , a ; a + 1 2 ; z ) by three approaches, applies the integral representation to give integral representations of several functions involving the inverse tangent function and including the Wilf function, and find out several combinatorial identities.

MSC 2020: 33C05; 30E20

Award Identifier / Grant number: 2025QN01041

Funding statement: The author was partially supported by the Natural Science Foundation of Inner Mongolia Autonomous Region (Grant No. 2025QN01041) and by the Youth Project of Hulunbuir City for Basic Research and Applied Basic Research (Grant No. GH2024020).

Acknowledgements

The author appreciates anonymous referees for their careful corrections, valuable comments, and helpful suggestions to the original version of this paper.

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Received: 2025-08-15
Revised: 2025-10-14
Accepted: 2025-10-16
Published Online: 2025-10-28

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 29.10.2025 von https://www.degruyterbrill.com/document/doi/10.1515/anly-2025-0066/pdf
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