Contiguous relations and summation and transformation formulas for basic hypergeometric series
arXiv:1304.5830
Abstract
By using contiguous relations for basic hypergeometric series, we give simple proofs of Bailey's summation, Carlitz's summation, Sears' to transformation, Sears' transformations, Chen's bibasic summation, Gasper's split poised transformation, Chu's bibasic symmetric transformation. Along the same line, finite forms of Sylvester's identity, Jacobi's triple product identity, and Kang's identity are also obtained.
14 pages, to appear in Journal of Difference Equations and Applications