Asymptotic expansions for certain multiple q-integrals and q-differentials of Thomae-Jackson type

Masanori Katsurada

doi:10.1063/1.3478171

Asymptotic expansions for certain multiple q-integrals and q-differentials of Thomae-Jackson type

Masanori Katsurada

Faculty of Economics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This is a summarized version of the forthcoming paper [11]. Let q be a complex parameter with |q| < 1. We shall study in this paper asymptotic aspects when q→1 of certain general classes of q-integral and q-differential operations given in (1.5) and (1.6) below respectively; this leads us to establish complete asymptotic expansions for their iterated extensions (Theorems 1 and 2) under fairly generic situations (Theorem 3). Several applications of of our main formulae (2.4) and (2.9) are further given for the generalized Lerch zeta-function defined by (3.3) (Theorems 4-6 and Corollary 6.1), the q-factorials (Corollary 4.1), q-analogues of the exponential (Corollary 4.2), the binomial (Corollary 4.3), and the poly-logarithmic functions (Corollaries 4.4 and 5.1).

Original language	English
Title of host publication	Diophantine Analysis and Related Fields 2010, DARF - 2010
Pages	100-113
Number of pages	14
DOIs	https://doi.org/10.1063/1.3478171
Publication status	Published - 2010 Aug 26
Event	Diophantine Analysis and Related Fields 2010, DARF 2010 - Musashino, Tokyo, Japan Duration: 2010 Mar 4 → 2010 Mar 5

Publication series

Name	AIP Conference Proceedings
Volume	1264
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Other

Other	Diophantine Analysis and Related Fields 2010, DARF 2010
Country/Territory	Japan
City	Musashino, Tokyo
Period	10/3/4 → 10/3/5

Keywords

Mellin-transform
asymptotic expansion
multiple q-differential
multiple q-integral

ASJC Scopus subject areas

Physics and Astronomy(all)

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10.1063/1.3478171

Cite this

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title = "Asymptotic expansions for certain multiple q-integrals and q-differentials of Thomae-Jackson type",

abstract = "This is a summarized version of the forthcoming paper [11]. Let q be a complex parameter with |q| < 1. We shall study in this paper asymptotic aspects when q→1 of certain general classes of q-integral and q-differential operations given in (1.5) and (1.6) below respectively; this leads us to establish complete asymptotic expansions for their iterated extensions (Theorems 1 and 2) under fairly generic situations (Theorem 3). Several applications of of our main formulae (2.4) and (2.9) are further given for the generalized Lerch zeta-function defined by (3.3) (Theorems 4-6 and Corollary 6.1), the q-factorials (Corollary 4.1), q-analogues of the exponential (Corollary 4.2), the binomial (Corollary 4.3), and the poly-logarithmic functions (Corollaries 4.4 and 5.1).",

keywords = "Mellin-transform, asymptotic expansion, multiple q-differential, multiple q-integral",

author = "Masanori Katsurada",

year = "2010",

month = aug,

day = "26",

doi = "10.1063/1.3478171",

language = "English",

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series = "AIP Conference Proceedings",

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T1 - Asymptotic expansions for certain multiple q-integrals and q-differentials of Thomae-Jackson type

AU - Katsurada, Masanori

PY - 2010/8/26

Y1 - 2010/8/26

N2 - This is a summarized version of the forthcoming paper [11]. Let q be a complex parameter with |q| < 1. We shall study in this paper asymptotic aspects when q→1 of certain general classes of q-integral and q-differential operations given in (1.5) and (1.6) below respectively; this leads us to establish complete asymptotic expansions for their iterated extensions (Theorems 1 and 2) under fairly generic situations (Theorem 3). Several applications of of our main formulae (2.4) and (2.9) are further given for the generalized Lerch zeta-function defined by (3.3) (Theorems 4-6 and Corollary 6.1), the q-factorials (Corollary 4.1), q-analogues of the exponential (Corollary 4.2), the binomial (Corollary 4.3), and the poly-logarithmic functions (Corollaries 4.4 and 5.1).

AB - This is a summarized version of the forthcoming paper [11]. Let q be a complex parameter with |q| < 1. We shall study in this paper asymptotic aspects when q→1 of certain general classes of q-integral and q-differential operations given in (1.5) and (1.6) below respectively; this leads us to establish complete asymptotic expansions for their iterated extensions (Theorems 1 and 2) under fairly generic situations (Theorem 3). Several applications of of our main formulae (2.4) and (2.9) are further given for the generalized Lerch zeta-function defined by (3.3) (Theorems 4-6 and Corollary 6.1), the q-factorials (Corollary 4.1), q-analogues of the exponential (Corollary 4.2), the binomial (Corollary 4.3), and the poly-logarithmic functions (Corollaries 4.4 and 5.1).

KW - Mellin-transform

KW - asymptotic expansion

KW - multiple q-differential

KW - multiple q-integral

UR - http://www.scopus.com/inward/record.url?scp=77955819965&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955819965&partnerID=8YFLogxK

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BT - Diophantine Analysis and Related Fields 2010, DARF - 2010

T2 - Diophantine Analysis and Related Fields 2010, DARF 2010

Y2 - 4 March 2010 through 5 March 2010

ER -

Asymptotic expansions for certain multiple q-integrals and q-differentials of Thomae-Jackson type

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Keywords

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