Article
Hybrid Proofs of the q-Binomial Theorem and Other Identities
Electronic Journal of Combinatorics
Document Type
Article
Publication Date
1-1-2011
Disciplines
- Education and
- Mathematics
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.
Citation Information
Dennis Eichhorn, James McLaughlin and Andrew Sills. "Hybrid Proofs of the q-Binomial Theorem and Other Identities" Electronic Journal of Combinatorics Vol. 18 Iss. 1 (2011) p. 1 - 21 ISSN: 1077-8926 Available at: http://works.bepress.com/andrew_sills/39/
This is a preprint of the final published article available at Electronic Journal of Combinatorics.