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TRANSFORMATION FORMULA OF DWORK’S p-ADIC HYPERGEOMETRIC FUNCTION

Part of: Other special functions

Published online by Cambridge University Press:  30 October 2025

YUSUKE NEMOTO Open the ORCID record for YUSUKE NEMOTO [Opens in a new window]
YUSUKE NEMOTO*
Affiliation:
Chiba University , Yayoicho 1-33, Inage 263-8522, Japan
*
e-mail: y-nemoto@waseda.jp
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Abstract

In this paper, we give a transformation formula of Dwork’s p-adic hypergeometric function between t and $t^{-1}$. As an appendix, we introduce a finite analogue of this transformation formula, which implies a special case of the transformation formula for Dwork’s p-adic hypergeometric function.

Keywords

Dwork’s p-adic hypergeometric functiontransformation formula

MSC classification

Primary: 33C20: Generalized hypergeometric series, $_pF_q$
Secondary: 33E50: Special functions in characteristic $p$ (gamma functions, etc.)

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 12
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc

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Footnotes

This paper is a part of the outcome of research performed under Waseda University Grant for Special Research Projects (Project number: 2024C-280) and Kakenhi Applicants (Project number: 2024R-054).

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