Bijective proofs of basic hypergeometric series identities

J. T. Joichi, Dennis Stanton

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

Bijections are given which prove the following theorems: the q-binomial theorem, Heine’s2Φ1 transformation, the q-analogues of Gauss’, Rummer’s, and Saalschütz’s theorems, the very well poised 4Φ3 and 6Φ5 evaluations, and Watson’s transformation of an 8Φ7 to a 4Φ3. The proofs hold for all values of the parameters. Bijective proofs of the terminating cases follow from the general case. A bijective version of limiting cases of these series is also given. The technique is to mimic the classical proofs, based upon a bijective proof of the q-binomial theorem and sign-reversing involutions which cancel infinite products.

Original languageEnglish (US)
Pages (from-to)103-120
Number of pages18
JournalPacific Journal of Mathematics
Volume127
Issue number1
DOIs
StatePublished - Mar 1987

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