On q-Raabe integral and some extensions

Mohamed El Bachraoui; József Sándor

doi:10.1007/s13398-020-00796-5

On q-Raabe integral and some extensions

Mohamed El Bachraoui
, József Sándor

Department of Mathematical Sciences

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

1 Citation (Scopus)

Abstract

The Raabe integral ∫01logΓq(x)dx for q-gamma function where 0 < q< 1 was obtained independently by Mahmoud and Agarwal as well as El Bachraoui. We obtain a third method for the computation of this integral. We extend further the q-Raabe integral by evaluating ∫01xklogΓq(x)dx for k= 0 , 1 , … providing q-analogues for ∫01xklogΓ(x)dx.

Original language	English
Article number	60
Journal	Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume	114
Issue number	2
DOIs	https://doi.org/10.1007/s13398-020-00796-5
Publication status	Published - Apr 1 2020

Keywords

Raabe formula
q-gamma function

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology
Computational Mathematics
Applied Mathematics

Access to Document

10.1007/s13398-020-00796-5

Cite this

@article{0e9733c30ac94677b067b2f6e0641575,

title = "On q-Raabe integral and some extensions",

abstract = "The Raabe integral ∫01logΓq(x)dx for q-gamma function where 0 < q< 1 was obtained independently by Mahmoud and Agarwal as well as El Bachraoui. We obtain a third method for the computation of this integral. We extend further the q-Raabe integral by evaluating ∫01xklogΓq(x)dx for k= 0 , 1 , … providing q-analogues for ∫01xklogΓ(x)dx.",

keywords = "Raabe formula, q-gamma function",

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

note = "Publisher Copyright: {\textcopyright} 2020, The Royal Academy of Sciences, Madrid.",

year = "2020",

month = apr,

day = "1",

doi = "10.1007/s13398-020-00796-5",

language = "English",

volume = "114",

journal = "Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas",

issn = "1578-7303",

publisher = "Springer-Verlag Italia s.r.l.",

number = "2",

}

TY - JOUR

T1 - On q-Raabe integral and some extensions

AU - Bachraoui, Mohamed El

AU - Sándor, József

PY - 2020/4/1

Y1 - 2020/4/1

N2 - The Raabe integral ∫01logΓq(x)dx for q-gamma function where 0 < q< 1 was obtained independently by Mahmoud and Agarwal as well as El Bachraoui. We obtain a third method for the computation of this integral. We extend further the q-Raabe integral by evaluating ∫01xklogΓq(x)dx for k= 0 , 1 , … providing q-analogues for ∫01xklogΓ(x)dx.

AB - The Raabe integral ∫01logΓq(x)dx for q-gamma function where 0 < q< 1 was obtained independently by Mahmoud and Agarwal as well as El Bachraoui. We obtain a third method for the computation of this integral. We extend further the q-Raabe integral by evaluating ∫01xklogΓq(x)dx for k= 0 , 1 , … providing q-analogues for ∫01xklogΓ(x)dx.

KW - Raabe formula

KW - q-gamma function

UR - https://www.scopus.com/pages/publications/85077707733

UR - https://www.scopus.com/pages/publications/85077707733#tab=citedBy

U2 - 10.1007/s13398-020-00796-5

DO - 10.1007/s13398-020-00796-5

M3 - Article

AN - SCOPUS:85077707733

SN - 1578-7303

VL - 114

JO - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas

JF - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas

IS - 2

M1 - 60

ER -

On q-Raabe integral and some extensions

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this