Geodesic
An extension to overpartitions of Rogers-Ramanujan identities for even moduli
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006).

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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. 
@article{DMTCS_2006_special_252_a22,
     author = {Corteel, Sylvie and Lovejoy, Jeremy and Mallet, Olivier},
     title = {An extension to overpartitions of {Rogers-Ramanujan} identities for even moduli},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities},
     year = {2006},
     doi = {10.46298/dmtcs.3498},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3498/}
}
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Corteel, Sylvie; Lovejoy, Jeremy; Mallet, Olivier. An extension to overpartitions of Rogers-Ramanujan identities for even moduli. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006). doi : 10.46298/dmtcs.3498. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3498/

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