Truncated Hypergeometric Functions and Discretized Integrals

2025/07/26 by Shûji Yamamoto, Yamamoto, Shuji
Mathematics · #33C05 (Primary) 11M32 (Secondary) #Advanced Mathematical Identities #Algebraic structures and combinatorial models #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2507.19793

openalex publication_date 2025/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a kind of finite truncation of the hypergeometric series and provide its discretized integral representation. This is motivated by recent results of Maesaka-Seki-Watanabe and Hirose-Matsusaka-Seki on the identity between truncated series and discretized integrals which comes from the mutliple zeta values and multiple polylogarithms. We also prove the formula of Ohno-Zagier type which relates the truncated multiple polylogarithms and the truncated hypergeometric series.

Citations

• A discretization of the iterated integral expression of the multiple polylogarithm
• Deriving two dualities simultaneously from a family of identities for multiple harmonic sums

Related

• Séries hypergéométriques multiples et polyzêtas
• Hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions
• Truncated Gauss hypergeometric series and its application in digamma function
• Two supercongruences involving truncated hypergeometric series
• p-adic analogues of hypergeometric identities