q-Fibonacci Polynomials and the Rogers-Ramanujan Identities
نویسندگان
چکیده
منابع مشابه
Basis partition polynomials, overpartitions and the Rogers-Ramanujan identities
In this paper, a common generalization of the Rogers-Ramanujan series and the generating function for basis partitions is studied. This leads naturally to a sequence of polynomials, called BsP-polynomials. In turn, the BsP-polynomials provide simultaneously a proof of the Rogers-Ramanujan identities and a new, more rapidly converging series expansion for the basis partition generating function....
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where a = 0 or 1, are among the most famous q-series identities in partitions and combinatorics. Since their discovery the Rogers-Ramanujan identities have been proved and generalized in various ways (see [2, 4, 5, 13] and the references cited there). In [13], by adapting a method of Macdonald for calculating partial fraction expansions of symmetric formal power series, Stembridge gave an unusu...
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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...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2004
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-004-0220-8