Proofs for certain Pi_q-conjectures of Gosper

2019/08/06 by Bing He, He, Bing
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1908.02010

openalex publication_date 2019/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 2001 W. Gosper introduced a constant Pi_q and conjectured without proofs many intriguing identities on this constant. In this paper we establish some modular equations of degrees 3 and 5. From these modular equations we confirm two groups of Pi_q-identities in Gosper's list. One group involves Pi_q,Pi_q²,Pi_q³ or Pi_q⁶ while the other is related to Pi_q,Pi_q²,Pi_q⁵ or Pi_q¹⁰.

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