WZ pairs and $q$-Analogues of Ramanujan series for $1/\pi$ (with an appendix by Wadim Zudilin)

TL;DR

This paper establishes q-analogues of two Ramanujan-type series for 1/π using q-analogues of WZ pairs, advancing the understanding of q-series and their relation to classical mathematical constants.

Contribution

It introduces novel q-analogues of Ramanujan series for 1/π derived from q-analogues of WZ pairs, providing new insights into q-series and special functions.

Findings

Proved q-analogues of two Ramanujan-type series for 1/π

Connected q-analogues with classical series through WZ pairs

Enhanced understanding of q-series in relation to mathematical constants

Abstract

We prove q-analogues of two Ramanujan-type series for $1/\pi$ from $q$-analogues of ordinary WZ pairs.