A Determinant Identity that Implies Rogers-Ramanujan

descriptionPublicationkeyboard_double_arrow_right Article 29 Jul 2005Publisher:The Electronic Journal of CombinatoricsJournal:The Electronic Journal of Combinatorics, volume 12 (eissn: 1077-8926,

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Authors: Kristina C. Garrett;

doi: 10.37236/1932

A Determinant Identity that Implies Rogers-Ramanujan

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Abstract

We give a combinatorial proof of a general determinant identity for associated polynomials. This determinant identity gives rise to new polynomial generalizations of known Rogers-Ramanujan type identities. Several examples of new Rogers-Ramanujan type identities are given.

Keywords

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Rogers-Ramanujan type identities, \(q\)-calculus and related topics, Orthogonal polynomials (combinatorics)

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