Abstract
The object of the paper is a thorough analysis of the WP-Bailey tree, a recent extension of classical Bailey chains. The paper begins by observing how the WP-Bailey tree naturally requires a finite number of classical q-hypergeometric transformation formulas. It then shows how to move beyond this closed set of results, and in the process, heretofore mysterious identities of Bressoud are explicated. Next, WP-Bailey pairs are used to provide a new proof of a recent formula of Kirillov. Finally, the relation between the approach in the paper and that of Burge is discussed.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 529-549 |
| Number of pages | 21 |
| Journal | Journal of the London Mathematical Society |
| Volume | 66 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jan 1 2002 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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The WP-Bailey tree and its implications. / Andrews, George E.; Berkovich, Alexander.
In: Journal of the London Mathematical Society, Vol. 66, No. 3, 01.01.2002, p. 529-549.Research output: Contribution to journal › Article
TY - JOUR
T1 - The WP-Bailey tree and its implications
AU - Andrews, George E.
AU - Berkovich, Alexander
PY - 2002/1/1
Y1 - 2002/1/1
N2 - The object of the paper is a thorough analysis of the WP-Bailey tree, a recent extension of classical Bailey chains. The paper begins by observing how the WP-Bailey tree naturally requires a finite number of classical q-hypergeometric transformation formulas. It then shows how to move beyond this closed set of results, and in the process, heretofore mysterious identities of Bressoud are explicated. Next, WP-Bailey pairs are used to provide a new proof of a recent formula of Kirillov. Finally, the relation between the approach in the paper and that of Burge is discussed.
AB - The object of the paper is a thorough analysis of the WP-Bailey tree, a recent extension of classical Bailey chains. The paper begins by observing how the WP-Bailey tree naturally requires a finite number of classical q-hypergeometric transformation formulas. It then shows how to move beyond this closed set of results, and in the process, heretofore mysterious identities of Bressoud are explicated. Next, WP-Bailey pairs are used to provide a new proof of a recent formula of Kirillov. Finally, the relation between the approach in the paper and that of Burge is discussed.
UR - http://www.scopus.com/inward/record.url?scp=0036948635&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036948635&partnerID=8YFLogxK
U2 - 10.1112/S0024610702003617
DO - 10.1112/S0024610702003617
M3 - Article
AN - SCOPUS:0036948635
VL - 66
SP - 529
EP - 549
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
SN - 0024-6107
IS - 3
ER -