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

研究成果: Conference contribution

抄録

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).

本文言語English
ホスト出版物のタイトルDiophantine Analysis and Related Fields 2010, DARF - 2010
ページ100-113
ページ数14
DOI
出版ステータスPublished - 2010 8月 26
イベントDiophantine Analysis and Related Fields 2010, DARF 2010 - Musashino, Tokyo, Japan
継続期間: 2010 3月 42010 3月 5

出版物シリーズ

名前AIP Conference Proceedings
1264
ISSN(印刷版)0094-243X
ISSN(電子版)1551-7616

Other

OtherDiophantine Analysis and Related Fields 2010, DARF 2010
国/地域Japan
CityMusashino, Tokyo
Period10/3/410/3/5

ASJC Scopus subject areas

  • 物理学および天文学(全般)

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