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

Mohamed E.L. Bachraoui

doi:10.1090/proc/14690

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

Mohamed E.L. Bachraoui

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 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 language	English
Pages (from-to)	4451-4464
Number of pages	14
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	10
DOIs	https://doi.org/10.1090/proc/14690
Publication status	Published - Jan 1 2019

Keywords

Integrals
Lambert series
Q-trigonometric functions
Ramanujan theta functions

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/proc/14690

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AB - 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.

KW - Integrals

KW - Lambert series

KW - Q-trigonometric functions

KW - Ramanujan theta functions

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

Abstract

Keywords

ASJC Scopus subject areas

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