A multilateral Bailey lemma and multiple Andrews–Gordon identities
نویسندگان
چکیده
منابع مشابه
Supernomial Coefficients , Bailey ’ S Lemma and Rogers – Ramanujan - Type Identities
An elementary introduction to the recently introduced A2 Bailey lemma for supernomial coefficients is presented. As illustration, some A2 q-series identities are (re)derived which are natural analogues of the classical (A1) Rogers–Ramanujan identities and their generalizations of Andrews and Bressoud. The intimately related, but unsolved problems of supernomial inversion, An−1 and higher level ...
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for |q| < 1. The fame of these identities lies not only in their beauty and fascinating history [17, 3], but also in their relevance to the theory of partitions and many other branches of mathematics and physics. In particular, MacMahon [27] and Schur [39] independently noted that the left-hand side of (1.1) is the generating function for partitions into parts with difference at least two, whil...
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An elliptic BCn generalization of the classical two parameter Bailey Lemma is proved, and a basic one parameter BCn Bailey Lemma is obtained as a limiting case. Several summation and transformation formulas associated with the root system BCn are proved as applications, including a 6φ5 summation formula, a generalized Watson transformation and an unspecialized Rogers–Selberg identity. The last ...
متن کاملA Higher-level Bailey Lemma
We propose a generalization of Bailey’s lemma, useful for proving q-series identities. As an application, generalizations of Euler’s identity, the Rogers–Ramanujan identities, and the Andrews–Gordon identities are derived. The generalized Bailey lemma also allows one to derive the branching functions of higher-level A (1) 1 cosets. 1. The Bailey Lemma In his famous 1949 paper, W. N. Bailey note...
متن کاملAN ELLIPTIC BCn BAILEY LEMMA AND ROGERS–RAMANUJAN IDENTITIES ASSOCIATED TO ROOT SYSTEMS
(1.2) (a; q)α := (a; q)∞ (aqα; q)∞ in terms of (a; q)∞ := ∏∞ i=0(1− aq ). These identities have a very rich history. Many important figures in mathematics had contributed to the development of these identities starting with Rogers [25] who first proved them in 1894, and Ramanujan [17] whose involvement made Rogers’ unnoticed work popular. Others contributed by simplifying existing proofs, sugge...
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ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2011
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-010-9275-9