Contiguous relations and summation and transformation formulas for basic hypergeometric series

Feng Gao, Victor J. W. Guo

By using contiguous relations for basic hypergeometric series, we give simple proofs of Bailey's ${}_4{\varphi }_3$ summation, Carlitz's ${}_5{\varphi }_4$ summation, Sears' ${}_3{\varphi }_2$ to ${}_5{\varphi }_4$ transform…