An Algebraic Identity

Abstract

An alternative proof of W. N. Bailey's identity may suggest how others of a similar nature can be systematically derived from the basic hypergeometric series. Among the analogues of theorems on the generalized hypergeometric series in the theory of the basic hypergeometric series are the transformations corresponding to Thomas's for the series ₃F₂. The proof of the identities by an interchange of order of summation for the case of the basic hypergeometric series is almost identical with that for the original case.

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