TY - JOUR

T1 - Bijective proofs of basic hypergeometric series identities

AU - Joichi, J. T.

AU - Stanton, Dennis

PY - 1987/3

Y1 - 1987/3

N2 - 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.

AB - 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.

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U2 - 10.2140/pjm.1987.127.103

DO - 10.2140/pjm.1987.127.103

M3 - Article

AN - SCOPUS:84972554387

VL - 127

SP - 103

EP - 120

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 1

ER -