Hybrid Proofs of the q-Binomial Theorem and Other Identities

Authors

Dennis Eichhorn, University of California
James McLaughlin, West Chester University of PennsylvaniaFollow
Andrew Sills, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

2011

Publication Title

Electronic Journal of Combinatorics

ISSN

1077-8926

Abstract

We give "hybrid" proofs of the q-binomial theorem and other identities. The proofs are "hybrid" in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the Identity Theorem) to prove the full version.

We prove three somewhat unusual summation formulae, and use these to give hybrid proofs of a number of identities due to Ramanujan.

Finally, we use these new summation formulae to give new partition interpretations of the Rogers-Ramanujan identities and the Rogers-Selberg identities.

Comments

This is a preprint of the final published article available at Electronic Journal of Combinatorics.

Recommended Citation

Eichhorn, Dennis, James McLaughlin, Andrew Sills. 2011. "Hybrid Proofs of the q-Binomial Theorem and Other Identities." Electronic Journal of Combinatorics, 18 (1): 1-21. source: http://www.combinatorics.org/Volume_18/PDF/v18i1p60.pdf
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/174