A limiting form of the q-Dixon_4\phi_3 summation and related partition identities
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- May 2002
- DOI:
- 10.48550/arXiv.math/0205031
- arXiv:
- arXiv:math/0205031
- Bibcode:
- 2002math......5031A
- Keywords:
-
- Mathematics - Combinatorics;
- Mathematics - Number Theory;
- Mathematics - Quantum Algebra;
- 05A17;
- 05A19;
- 11P83;
- 11P81;
- 33D15;
- 33D20
- E-Print:
- 12 pages