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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On series identities of Gosper and integrals of Ramanujan theta function $\psi (q)$
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by Mohamed El Bachraoui PDF
Proc. Amer. Math. Soc. 147 (2019), 4451-4464 Request permission

Abstract:

We prove some Lambert series identities which were stated by Gosper without proof or reference. As an application we shall evaluate integrals involving Ramanujan theta function $\psi (q)$. Furthermore, motivated by Ramanujan identities for $q\psi ^4(q^2)$ and $\frac {\psi ^3(q)}{\psi (q^3)}$, we shall evaluate the squares of $q\psi ^4(q^2)$ and $\frac {\psi ^3(q)}{\psi (q^3)}$ in terms of Lambert series.
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Additional Information
  • Mohamed El Bachraoui
  • Affiliation: Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al-Ain, United Arab Emirates
  • MR Author ID: 708599
  • Email: melbachraoui@uaeu.ac.ae
  • Received by editor(s): January 31, 2019
  • Published electronically: June 14, 2019
  • Communicated by: Mourad Ismail
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4451-4464
  • MSC (2010): Primary 33E05, 11F11, 11F12
  • DOI: https://doi.org/10.1090/proc/14690
  • MathSciNet review: 4002555