Exploring Rogers-Ramanujan-Type Identities Modulo 9, 11, 18, and 22
DOI:
https://doi.org/10.53469/jrve.2025.7(02).01Keywords:
Rogers-Ramanujan Type Identities, Jacobi’s Triple Product Identity, Bailey PairsAbstract
In this paper, some identities of Rogers_Ramanujan Type related to modulo 9, 11, 18 and 22 is derived with the incorporation of generalized Bailey pairs and some standard results established by Andrew V. Sills [1] using some q − difference relations.
References
Andrew V. Sills, "On Identities of the Rogers- Ramanujan Type". Ramanujan journal, 1-28 (2004)
G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University press1990.
G.E. Andrews, "Encyclopedia of Mathematics and its application",(Ed: Gian- Carlo Rota (ed.)2, The Theory of partitions, Addison Wesley co., Newyork 1976.
I Scur, "Ein Beitrag zur additive Zahlen und zur Theorie der Kettenbruche", Sitzungsberichte der Berliner Akademie (1917), 302-321
L.J. Slater, Further Identities of Rogers Ramanujan Type, Proc. London Math. Soc. 54 (1952) 147-167.
L. J. Rogers, Second memoir on the expansion of certain infinite products, Proc. London Math. Soc. 25 (1894), pp, 318-343.
P.A. MacMahon, Combinatory Analysis, vol. 2, Cambridge University Press, London 1918.
W.N. Bailey, "Some identities in combinatory analysis," Proc. London Math. Soc.(2), 49 (1947),421- 435.
W.N. Bailey, "Identities of Rogers-Ramanujan Type"
Proc. London Math. Soc.(2), 50 (1949), 1-10
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