Contiguous relations of ${}_3{\varphi }_2$-series

Abstract

According to Abel's lemma and the method of linear combinations, we establish numerous contiguous relations of ${}_3{\varphi }_2$-series, which can be regarded as q-analogues of the contiguous relations of ${}_3{F}_2$-series due to Krattenthaler and Rivoal [12] or Chu and Wang [4].