Iteration method for multiple Rogers-Ramanujan identities
نویسندگان
چکیده
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.
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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...
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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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Recently, many q-identities from Slater’s compendium [S] have been interpreted combinatorially by several authors (e.g., see Connor [lo], Subbarao [9], Agarwal [l], and Agarwal and Andrews [2]). In his very recent paper [6], Andrews gave combinatorial interpretations of the Gessel-Stanton q-identities in terms of two-color paritions and expressed the hope that other q-identities such as those i...
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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: Kodai Mathematical Journal
سال: 2009
ISSN: 0386-5991
DOI: 10.2996/kmj/1257948891