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An extension to overpartitions of Rogers-Ramanujan identities for even moduli
Abstract : We investigate class of well-poised basic hypergeometric series $\tilde{J}_{k,i}(a;x;q)$, interpreting these series as generating functions for overpartitions defined by multiplicity conditions. We also show how to interpret the $\tilde{J}_{k,i}(a;1;q)$ as generating functions for overpartitions whose successive ranks are bounded, for overpartitions that are invariant under a certain class of conjugations, and for special restricted lattice paths. We highlight the cases $(a,q) \to (1/q,q)$, $(1/q,q^2)$, and $(0,q)$, where some of the functions $\tilde{J}_{k,i}(a;x;q)$ become infinite products. The latter case corresponds to Bressoud's family of Rogers-Ramanujan identities for even moduli.
Cited literature [24 references]
https://hal.inria.fr/hal-01184702
Contributor : Coordination Episciences Iam <>
Submitted on : Monday, August 17, 2015 - 2:24:22 PM
Last modification on : Thursday, July 8, 2021 - 3:49:52 AM
Long-term archiving on: : Wednesday, November 18, 2015 - 12:08:52 PM
Contributor : Coordination Episciences Iam <>
Submitted on : Monday, August 17, 2015 - 2:24:22 PM
Last modification on : Thursday, July 8, 2021 - 3:49:52 AM
Long-term archiving on: : Wednesday, November 18, 2015 - 12:08:52 PM
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