منابع مشابه
New Finite Rogers-Ramanujan Identities
We present two general finite extensions for each of the two Rogers-Ramanujan identities. Of these one can be derived directly from Watson’s transformation formula by specialization or through Bailey’s method, the second similar formula can be proved either by using the first formula and the q-Gosper algorithm, or through the so-called Bailey lattice.
متن کاملFinite Rogers-Ramanujan Type Identities
Polynomial generalizations of all 130 of the identities in Slater’s list of identities of the Rogers-Ramanujan type are presented. Furthermore, duality relationships among many of the identities are derived. Some of the these polynomial identities were previously known but many are new. The author has implemented much of the finitization process in a Maple package which is available for free do...
متن کاملVariants of the Rogers-ramanujan Identities
We evaluate several integrals involving generating functions of continuous q-Hermite polynomials in two diierent ways. The resulting identities give new proofs and generalizations of the Rogers-Ramanujan identities. Two quintic transformations are given, one of which immediately proves the Rogers-Ramanujan identities without the Jacobi triple product identity. Similar techniques lead to new tra...
متن کاملRefinements of the Rogers-Ramanujan Identities
Refinements of the classical Rogers-Ramanujan identities are given in which some parts are weighted. Combinatorial interpretations refining MacMahon’s results are corollaries.
متن کاملRogers-ramanujan Type Identities for Alternating Knots
We highlight the role of q-series techniques in proving identities arising from knot theory. In particular, we prove Rogers-Ramanujan type identities for alternating knots as conjectured by Garoufalidis, Lê and Zagier.
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ژورنال
عنوان ژورنال: Turkish Journal of Analysis and Number Theory
سال: 2016
ISSN: 2333-1100
DOI: 10.12691/tjant-3-2-1