A Family of Theta-Function Identities Based upon Combinatorial Partition Identities Related to Jacobi’s Triple-Product Identity

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dc.contributor.authorSrivastava, H.M.
dc.contributor.authorSrivastava, Rekha
dc.contributor.authorChaudhary, Mahendra Pal
dc.contributor.authorUddin, Salah
dc.date.accessioned2020-07-10T16:56:26Z
dc.date.available2020-07-10T16:56:26Z
dc.date.copyright2020en_US
dc.date.issued2020
dc.description.abstractThe authors establish a set of six new theta-function identities involving multivariable R-functions which are based upon a number of q-product identities and Jacobi’s celebrated triple-product identity. These theta-function identities depict the inter-relationships that exist among theta-function identities and combinatorial partition-theoretic identities. Here, in this paper, we consider and relate the multivariable R-functions to several interesting q-identities such as (for example) a number of q-product identities and Jacobi’s celebrated triple-product identity. Various recent developments on the subject-matter of this article as well as some of its potential application areas are also briefly indicated. Finally, we choose to further emphasize upon some close connections with combinatorial partition-theoretic identities and present a presumably open problem.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.description.sponsorshipThis research received no external funding.en_US
dc.identifier.citationSrivastava, H. M., Srivastava, R., Chaudhary, M. P., & Uddin, S. (2020). A family of theta-function identities based upon combinatorial partition identities related to Jacobi’s triple-product identity. Mathematics, 8(6). https://doi.org/10.3390/math8060918en_US
dc.identifier.urihttps://doi.org/10.3390/math8060918
dc.identifier.urihttp://hdl.handle.net/1828/11921
dc.language.isoenen_US
dc.publisherMathematicsen_US
dc.subjecttheta-function identitiesen_US
dc.subjectmultivariable R-functionsen_US
dc.subjectJacobi's triple-product identityen_US
dc.subjectRamanujan's theta functionsen_US
dc.subjectq-product identitiesen_US
dc.subjectEuler's pentagonal number theoremen_US
dc.subjectRogers-Ramanujan continued fractionen_US
dc.subjectRogers-Ramanujan identitiesen_US
dc.subjectcombinatorial partition-theoreticen_US
dc.subjectSchur’s, the Göllnitz-Gordon’s and the Göllnitz’s partition identitiesen_US
dc.subjectSchur’s second partition theoremen_US
dc.titleA Family of Theta-Function Identities Based upon Combinatorial Partition Identities Related to Jacobi’s Triple-Product Identityen_US
dc.typeArticleen_US

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