Proofs for certain Pi_{q}-conjectures of Gosper
Classical Analysis and ODEs
2020-11-30 v5 Number Theory
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_{q^{2}},Pi_{q^{3}} or Pi_{q^{6}} while the other is related to Pi_{q},Pi_{q^{2}},Pi_{q^{5}} or Pi_{q^{10}}.
Keywords
Cite
@article{arxiv.1908.02010,
title = {Proofs for certain Pi_{q}-conjectures of Gosper},
author = {Bing He},
journal= {arXiv preprint arXiv:1908.02010},
year = {2020}
}
Comments
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