Continued fraction proofs of m-versions of some identities of Rogers–Ramanujan–Slater type
Source: The Ramanujan Journal, Volume 25, Number 2, June 2011 , pp. 203-227(25)
Abstract:We derive two general transformations for certain basic hypergeometric series from the recurrence formulae for the partial numerators and denominators of two q-continued fractions previously investigated by the authors.
By then specializing certain free parameters in these transformations, and employing various identities of Rogers–Ramanujan type, we derive m-versions of these identities. Some of the identities thus found are new, and some have been derived previously by other authors, using different methods.
By applying certain transformations due to Watson, Heine and Ramanujan, we derive still more examples of such m-versions of Rogers–Ramanujan-type identities.
Document Type: Research Article
Affiliations: 1: Mathematical Sciences, Northern Illinois University, DeKalb, IL, 60115-2888, USA, Email: firstname.lastname@example.org 2: Mathematics Department, West Chester University, 25 University Avenue, West Chester, PA, 19383, USA, Email: email@example.com 3: Mathematics Department, Trinity College, 300 Summit Street, Hartford, CT, 06106-3100, USA, Email: firstname.lastname@example.org
Publication date: June 1, 2011