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

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
Title of host publicationAIP Conference Proceedings
Pages100-113
Number of pages14
Volume1264
DOIs
Publication statusPublished - 2010
EventDiophantine Analysis and Related Fields 2010, DARF 2010 - Musashino, Tokyo, Japan
Duration: 2010 Mar 42010 Mar 5

Other

OtherDiophantine Analysis and Related Fields 2010, DARF 2010
CountryJapan
CityMusashino, Tokyo
Period10/3/410/3/5

Fingerprint

theorems
expansion
factorials
analogs

Keywords

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

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Asymptotic expansions for certain multiple q-integrals and q-differentials of Thomae-Jackson type. / Katsurada, Masanori.

AIP Conference Proceedings. Vol. 1264 2010. p. 100-113.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Katsurada, M 2010, Asymptotic expansions for certain multiple q-integrals and q-differentials of Thomae-Jackson type. in AIP Conference Proceedings. vol. 1264, pp. 100-113, Diophantine Analysis and Related Fields 2010, DARF 2010, Musashino, Tokyo, Japan, 10/3/4. https://doi.org/10.1063/1.3478171
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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).

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