TY - GEN

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

U2 - 10.1063/1.3478171

DO - 10.1063/1.3478171

M3 - Conference contribution

AN - SCOPUS:77955819965

SN - 9780735408159

T3 - AIP Conference Proceedings

SP - 100

EP - 113

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 -