A New Proof of the (H.2) Supercongruence of Van Hamme by a WZ Pair
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Keywords

WZ pair
Supercongruence
p-adic Gamma function

DOI

10.26689/ssr.v7i4.10173

Submitted : 2025-04-09
Accepted : 2025-04-24
Published : 2025-05-09

Abstract

This paper presents a new proof of Van Hamme’s supercongruence (H.2) using the WZ method, combining transformation and summation of WZ pairs and the properties of the p-adic Gamma function. Moreover, under the condition p ≡ 3 (mod 4), the study proves a supercongruence modulo p3.

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