General Wp-bailey Chains
نویسندگان
چکیده
Motivated by a recent paper of Liu and Ma, we describe a number of general WP-Bailey chains. We show that many of the existing WP-Bailey chains (or branches of the WP-Bailey tree), including chains found by Andrews, Warnaar and Liu and Ma, arise as special cases of these general WP-Bailey chains. We exhibit three new branches of the WP-Bailey tree, branches which also follow as special cases of these general WP-Bailey chains. Finally, we describe a number of new transformation formulae for basic hypergeometric series which arise as consequences of these new WP-Bailey chains.
منابع مشابه
The Wp – Bailey
Abstract. Our object is a thorough analysis of the WP-Bailey tree, a recent extension of classical Bailey chains. We begin by observing how the WP–Bailey tree naturally entails a finite number of classical q-hypergeometric transformation formulas. We then show how to move beyond this closed set of results and in the process we explicate heretofore mysterious identities of D. Bressoud. Next, we ...
متن کاملThe Wp – Bailey Tree and Its Implications
Abstract. Our object is a thorough analysis of the WP-Bailey tree, a recent extension of classical Bailey chains. We begin by observing how the WP–Bailey tree naturally entails a finite number of classical q-hypergeometric transformation formulas. We then show how to move beyond this closed set of results and in the process we explicate heretofore mysterious identities of D.M. Bressoud. Next, w...
متن کاملA Reciprocity Relation for Wp-bailey Pairs
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 CURIOUS q-SUMMATION FORMULAE
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...
متن کاملSome Implications of the Wp-bailey Tree
We consider a special case of a WP-Bailey chain of George Andrews, and use it to derive a number of curious transformations of basic hypergeometric series. We also derive two new WP-Bailey pairs, and use them to derive some new transformations for basic hypergeometric series. Finally, we briefly consider the implications of WP-Bailey pairs (αn(a, k), βn(a, k)), in which αn(a, k) is independent ...
متن کامل