On series identities of gosper and integrals of Ramanujan theta function ψ(q)

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6 Citations (Scopus)

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 ψ(q). Furthermore, motivated by Ramanujan identities for qψ4(q2) and ψ ψ 3 (q ( 3 q ) ), we shall evaluate the squares of qψ4(q2) and ψ ψ 3 (q ( 3 q ) ) in terms of Lambert series.

Original languageEnglish
Pages (from-to)4451-4464
Number of pages14
JournalProceedings of the American Mathematical Society
Volume147
Issue number10
DOIs
Publication statusPublished - 2019

Keywords

  • Integrals
  • Lambert series
  • Q-trigonometric functions
  • Ramanujan theta functions

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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