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

Published online by Cambridge University Press:  17 September 2020

SHANE CHERN
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA shanechern@psu.edu
DAZHAO TANG
Affiliation:
Center for Applied Mathematics, Tianjin University, Tianjin 300072, P. R. China
Corresponding

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.

Type
Research Article
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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