On a theta product of Jacobi and its applications to q-gamma products

Mohamed El Bachraoui; József Sándor

doi:10.1016/j.jmaa.2018.11.051

On a theta product of Jacobi and its applications to q-gamma products

Mohamed El Bachraoui
, József Sándor

Department of Mathematical Sciences

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

3 Citations (Scopus)

Abstract

We give a new proof for a product formula of Jacobi which turns out to be equivalent to a q-trigonometric product which was stated without proof by Gosper. We apply this formula to derive a q-analogue for the Gauss multiplication formula for the gamma function. Furthermore, we give explicit formulas for short products of q-gamma functions.

Original language	English
Pages (from-to)	814-826
Number of pages	13
Journal	Journal of Mathematical Analysis and Applications
Volume	472
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2018.11.051
Publication status	Published - Apr 1 2019

Keywords

Jacobi theta functions
q-Analogue
q-Gamma function
q-Trigonometric functions

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2018.11.051

Cite this

@article{5437d2a561fd4bd29b6ec7fdc46dc4c1,

title = "On a theta product of Jacobi and its applications to q-gamma products",

abstract = "We give a new proof for a product formula of Jacobi which turns out to be equivalent to a q-trigonometric product which was stated without proof by Gosper. We apply this formula to derive a q-analogue for the Gauss multiplication formula for the gamma function. Furthermore, we give explicit formulas for short products of q-gamma functions.",

keywords = "Jacobi theta functions, q-Analogue, q-Gamma function, q-Trigonometric functions",

author = "\{El Bachraoui\}, Mohamed and J{\'o}zsef S{\'a}ndor",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2019",

month = apr,

day = "1",

doi = "10.1016/j.jmaa.2018.11.051",

language = "English",

volume = "472",

pages = "814--826",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - On a theta product of Jacobi and its applications to q-gamma products

AU - El Bachraoui, Mohamed

AU - Sándor, József

PY - 2019/4/1

Y1 - 2019/4/1

N2 - We give a new proof for a product formula of Jacobi which turns out to be equivalent to a q-trigonometric product which was stated without proof by Gosper. We apply this formula to derive a q-analogue for the Gauss multiplication formula for the gamma function. Furthermore, we give explicit formulas for short products of q-gamma functions.

AB - We give a new proof for a product formula of Jacobi which turns out to be equivalent to a q-trigonometric product which was stated without proof by Gosper. We apply this formula to derive a q-analogue for the Gauss multiplication formula for the gamma function. Furthermore, we give explicit formulas for short products of q-gamma functions.

KW - Jacobi theta functions

KW - q-Analogue

KW - q-Gamma function

KW - q-Trigonometric functions

UR - https://www.scopus.com/pages/publications/85057017818

UR - https://www.scopus.com/pages/publications/85057017818#tab=citedBy

U2 - 10.1016/j.jmaa.2018.11.051

DO - 10.1016/j.jmaa.2018.11.051

M3 - Article

AN - SCOPUS:85057017818

SN - 0022-247X

VL - 472

SP - 814

EP - 826

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

On a theta product of Jacobi and its applications to q-gamma products

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this