A new proof of Andrews' conjecture for ${}_4{\varphi }_3$-series

Abstract

In terms of Sear's transformation formula for ${}_4{\varphi }_3$-series, we give new proofs of a summation formula for ${}_4{\varphi }_3$-series due to Andrews [2] and another summation formula for${}_4{\varphi }_3$-series conjectured in the same paper. Meanwhile, other several related results are also derived.