منابع مشابه
Lifting Bailey pairs to WP-Bailey pairs
A pair of sequences (αn(a, k, q),βn(a, k, q)) such that α0(a, k, q) = 1 and βn(a, k, q) = n ∑ j=0 (k/a; q)n−j(k; q)n+j (q; q)n−j(aq; q)n+j αj(a, k, q) is termed a WP-Bailey Pair. Upon setting k = 0 in such a pair we obtain a Bailey pair. In the present paper we consider the problem of “lifting” a Bailey pair to a WPBailey pair, and use some of the new WP-Bailey pairs found in this way to derive...
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We derive a new general transformation for WP-Bailey pairs by considering the a certain limiting case of a WP-Bailey chain previously found by the authors, and examine several consequences of this new transformation. These consequences include new summation formulae involving WP-Bailey pairs. Other consequences include new proofs of some classical identities due to Jacobi, Ramanujan and others,...
متن کاملSome Further Transformations for Wp-bailey Pairs
Let (αn(a, k), βn(a, k)) be a WP-Bailey pair. Assuming the limits exist, let (α n(a), β ∗ n(a)) = lim k→1 ( αn(a, k), βn(a, k) 1− k ) be the derived WP-Bailey pair. By considering a particular limiting case of a transformation due to George Andrews, we derive some transformation and summation formulae for derived WP-Bailey pairs. We then use the formula to derive new identities for various thet...
متن کاملBailey Pairs and Indefinite Quadratic Forms
We construct classes of Bailey pairs where the exponent of q in αn is an indefinite quadratic form. As an application we obtain families of q-hypergeometric mock theta multisums.
متن کاملN = 2 Supersymmetry and Bailey Pairs
We demonstrate that the Bailey pair formulation of Rogers-Ramanujan identities unifies the calculations of the characters of N = 1 and N = 2 supersymmetric conformal field theories with the counterpart theory with no supersymmetry. We illustrate this construction for the M(3, 4) (Ising) model where the Bailey pairs have been given by Slater. We then present the general unitary case. We demonstr...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.03.015