Certain derived WP-bailey pairs and transformation formulas for q-hypergeometric series
نویسندگان
چکیده
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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Abstract. We study multivariable (bilateral) basic hypergeometric series associated with (type A) Macdonald polynomials. We derive several transformation and summation properties for such series, including analogues of Heine’s 2φ1 transformation, the q-Pfaff-Kummer and Euler transformations, the q-Saalschütz summation formula, and Sear’s transformation for terminating, balanced 4φ3 series. For ...
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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,...
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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...
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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. Another consequence is a rather unusual summation formulae in which one side is an infinite basic-hyper...
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ژورنال
عنوان ژورنال: Filomat
سال: 2017
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1714619s