A limiting form of the q-Dixon_4ϕ_3 summation and related partition identities

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By considering a limiting form of the q-Dixon_4ϕ_3 summation, we prove a weighted partition theorem involving odd parts differing by >= 4. A two parameter refinement of this theorem is then deduced from a quartic reformulation of Goellnitz's (Big) theorem due to Alladi, and this leads to a two parameter extension of Jacobi's triple product identity for theta functions. Finally, refinements of certain modular identities of Alladi connected to the Goellnitz-Gordon series are shown to follow from a limiting form of the q-Dixon_4ϕ_3 summation.
12 pages

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Combinatorics, Number Theory, Quantum Algebra, 05A17, 05A19, 11P83, 11P81, 33D15, 33D20

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http://salesiana.dossiersoluciones.com/handle/123456789/63972

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0205031
 http://arxiv.org/abs/math/0205031

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arXiv