A limiting form of the q-Dixon_4\phi_3 summation and related partition identities
Combinatorics
2007-05-23 v1 Number Theory
Quantum Algebra
Abstract
By considering a limiting form of the q-Dixon_4\phi_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_4\phi_3 summation.
Keywords
Cite
@article{arxiv.math/0205031,
title = {A limiting form of the q-Dixon_4\phi_3 summation and related partition identities},
author = {Krishnaswami Alladi and Alexander Berkovich},
journal= {arXiv preprint arXiv:math/0205031},
year = {2007}
}
Comments
12 pages