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Transformation and summation formulas for basic hypergeometric series associated with the circumference ratio

Authors :
Wei, Chuanan
Publication Year :
2019

Abstract

In terms of the difference operators, we establish several curious transformation and summation formulas for basic hypergeometric series. When the parameters are specified, they produce $q$-analogues of Ramanujan's three series for 1/$\pi$ and other eleven nice $\pi$-formulas. Meanwhile, $q$-analogues of three beautiful series for $\zeta(3)$ are also given in the same way.<br />Comment: Some formulas of the paper has been given in a published paper

Subjects

Subjects :
Mathematics - Combinatorics

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1904.01767
Document Type :
Working Paper