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THE ROGERS–RAMANUJAN CONTINUED FRACTION AND RELATED ETA-QUOTIENT REPRESENTATIONS

Part of: Additive number theory; partitions Elementary number theory

Published online by Cambridge University Press:  17 September 2020

SHANE CHERN Open the ORCID record for SHANE CHERN [Opens in a new window]  and
DAZHAO TANG
SHANE CHERN
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USAshanechern@psu.edu
DAZHAO TANG*
Affiliation:
Center for Applied Mathematics, Tianjin University, Tianjin300072, P. R.China
*
e-mail: dazhaotang@sina.com
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Abstract

We construct eta-quotient representations of two families of q-series involving the Rogers–Ramanujan continued fraction by establishing related recurrence relations. We also display how these eta-quotient representations can be utilised to dissect certain q-series identities.

Keywords

Rogers–Ramanujan continued fractioneta-quotient representationsrecurrence relations

MSC classification

Primary: 11P84: Partition identities; identities of Rogers-Ramanujan type
Secondary: 11A55: Continued fractions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 2 , April 2021 , pp. 248 - 259
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

The second author was supported by the Postdoctoral Science Foundation of China (No. 2019M661005) and the Fundamental Research Funds for the Central Universities (No. 2018CDXYST0024).

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