A Standard Proof of Andrews’ Conjecture for ${}_4{\varphi }_3$-Series

Abstract

In terms of Sears’ transformation formula for ${}_4{\varphi }_3$-series, we provide standard proofs of a summation formula for ${}_4{\varphi }_3$-series due to Andrews [Andrews, Adv. Appl. Math. $46(2011),15-24]$ and another summation formula for ${}_4{\varphi }_3$-series conjectured in the same paper. Meanwhile, several other related results are also derived.