Supercongruences for a truncated hypergeometric series

2010/07/22 by Roberto Tauraso, Tauraso, Roberto · 1 citation
Mathematics · #11A07 #11B65 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1007.3852

openalex publication_date 2010/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this note is to obtain some congruences modulo a power of a prime p involving the truncated hypergeometric series ∑_k=1^p-1 (x)_k(1-x)_k\over (1)_k²⋅1\over k^a for a=1 and a=2. In the last section, the special case x=1/2 is considered.

Cited by

• Generalized Legendre polynomials and related congruences modulo p²

Related

• On supercongruences for truncated sums of squares of basic hypergeometric series
• Some supercongruences of arbitrary length
• Two supercongruences involving truncated hypergeometric series
• An extension of a supercongruence of Long and Ramakrishna
• Supercongruences arising from hypergeometric series identities