Abstract
A generalized Bailey pair, which contains several special cases considered by Bailey (Proc. London Math. Soc. (2), 50, 421-435 (1949)), is derived and used to find a number of new Rogers-Ramanujan type identities. Consideration of associated q-difference equations points to a connection with a mild extension of Gordon's combinatorial generalization of the Rogers-Ramanujan identities (Amer. J. Math., 83, 393-399 (1961)). This, in turn, allows the formulation of natural combinatorial interpretations of many of the identities in Slater's list (Proc. London Math. Soc. (2) 54, 147-167 (1952)), as well as the new identities presented here. A list of 26 new double sum-product Rogers-Ramanujan type identities are included as an Appendix.
Original language | English |
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Pages (from-to) | 403-429 |
Number of pages | 27 |
Journal | Ramanujan Journal |
Volume | 11 |
Issue number | 3 |
DOIs | |
State | Published - Jun 2006 |
Keywords
- Bailey pairs
- Partitions
- Rogers-Ramanujan identities