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Abel’s method on summation by parts and terminating well-poised \(q\)-series identities. (English) Zbl 1123.33013

The authors employ Abel’s lemma on summation by parts to give new proofs of some summation formulas of Jackson, Bailey, Carlitz, Bressoud, and Guo for terminating well-poised \(_3\phi_2\), \(_4\phi_3\), and \(_5\phi_4\) series The authors characterize this approach as “more simple and accessible to readers” than other known proofs and they emphasize that Abel’s lemma on summation by parts “is indeed a very natural choice for working with basic hypergeometric series.”

MSC:

33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
05A30 \(q\)-calculus and related topics
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References:

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