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

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 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

Access to Document

10.1090/proc/14690

Cite this

@article{04ef806c9706412c8867cca872621047,

title = "On series identities of gosper and integrals of Ramanujan theta function ψ(q)",

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.",

keywords = "Integrals, Lambert series, Q-trigonometric functions, Ramanujan theta functions",

author = "Bachraoui, {Mohamed E.L.}",

year = "2019",

month = jan,

day = "1",

doi = "10.1090/proc/14690",

language = "English",

volume = "147",

pages = "4451--4464",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "10",

}

TY - JOUR

T1 - On series identities of gosper and integrals of Ramanujan theta function ψ(q)

AU - Bachraoui, Mohamed E.L.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=85073333303&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073333303&partnerID=8YFLogxK

U2 - 10.1090/proc/14690

DO - 10.1090/proc/14690

M3 - Article

AN - SCOPUS:85073333303

SN - 0002-9939

VL - 147

SP - 4451

EP - 4464

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 10

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this