On a formula of the q-series 2k+4ϕ2k+3 and its applications

George E. Andrews; Mohamed El Bachraoui

doi:10.1007/s11139-025-01044-3

On a formula of the q-series 2k+4ϕ2k+3 and its applications

George E. Andrews, Mohamed El Bachraoui

Department of Mathematical Sciences

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

1 Citation (Scopus)

Abstract

In this paper we apply a formula of the very-well poised 2k+4ϕ2k+3 to write a k-tuple sum of q-series as a linear combination of terms wherein each term is a product of expressions of the form 1(qy,qy-1;q)∞. As an application, we shall express a variety of sums and double sums of q-series as linear combinations of infinite products. Our formulas are motivated by their connection to overpartition pairs.

Original language	English
Article number	79
Journal	Ramanujan Journal
Volume	66
Issue number	4
DOIs	https://doi.org/10.1007/s11139-025-01044-3
Publication status	Published - Apr 2025

Keywords

Basic hypergeometric series
Very-well poised

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1007/s11139-025-01044-3

Cite this

@article{f15df01580734f15936df3d6537a85a0,

title = "On a formula of the q-series 2k+4ϕ2k+3 and its applications",

abstract = "In this paper we apply a formula of the very-well poised 2k+4ϕ2k+3 to write a k-tuple sum of q-series as a linear combination of terms wherein each term is a product of expressions of the form 1(qy,qy-1;q)∞. As an application, we shall express a variety of sums and double sums of q-series as linear combinations of infinite products. Our formulas are motivated by their connection to overpartition pairs.",

keywords = "Basic hypergeometric series, Very-well poised",

author = "Andrews, \{George E.\} and \{El Bachraoui\}, Mohamed",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.",

year = "2025",

month = apr,

doi = "10.1007/s11139-025-01044-3",

language = "English",

volume = "66",

journal = "Ramanujan Journal",

issn = "1382-4090",

publisher = "Springer Netherlands",

number = "4",

}

TY - JOUR

T1 - On a formula of the q-series 2k+4ϕ2k+3 and its applications

AU - Andrews, George E.

AU - El Bachraoui, Mohamed

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

PY - 2025/4

Y1 - 2025/4

N2 - In this paper we apply a formula of the very-well poised 2k+4ϕ2k+3 to write a k-tuple sum of q-series as a linear combination of terms wherein each term is a product of expressions of the form 1(qy,qy-1;q)∞. As an application, we shall express a variety of sums and double sums of q-series as linear combinations of infinite products. Our formulas are motivated by their connection to overpartition pairs.

AB - In this paper we apply a formula of the very-well poised 2k+4ϕ2k+3 to write a k-tuple sum of q-series as a linear combination of terms wherein each term is a product of expressions of the form 1(qy,qy-1;q)∞. As an application, we shall express a variety of sums and double sums of q-series as linear combinations of infinite products. Our formulas are motivated by their connection to overpartition pairs.

KW - Basic hypergeometric series

KW - Very-well poised

UR - http://www.scopus.com/inward/record.url?scp=85218983475&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85218983475&partnerID=8YFLogxK

U2 - 10.1007/s11139-025-01044-3

DO - 10.1007/s11139-025-01044-3

M3 - Article

AN - SCOPUS:85218983475

SN - 1382-4090

VL - 66

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 4

M1 - 79

ER -

On a formula of the q-series 2k+4ϕ2k+3 and its applications

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this