Contiguous relations and summation and transformation formulas for basic hypergeometric series
Abstract
By using contiguous relations for basic hypergeometric series, we give simple proofs of Bailey's 4φ3 summation, Carlitz's 5φ4 summation, Sears' 3φ2 to 5φ4 transformation, Sears' 4φ3 transformations, Chen's bibasic summation, Gasper's split poised 10φ9 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.
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