### 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 |
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Title of host publication | AIP Conference Proceedings |

Pages | 100-113 |

Number of pages | 14 |

Volume | 1264 |

DOIs | |

Publication status | Published - 2010 |

Event | Diophantine Analysis and Related Fields 2010, DARF 2010 - Musashino, Tokyo, Japan Duration: 2010 Mar 4 → 2010 Mar 5 |

### Other

Other | Diophantine Analysis and Related Fields 2010, DARF 2010 |
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Country | Japan |

City | Musashino, Tokyo |

Period | 10/3/4 → 10/3/5 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*AIP Conference Proceedings*(Vol. 1264, pp. 100-113) https://doi.org/10.1063/1.3478171

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

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

*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

}

TY - GEN

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

AU - Katsurada, Masanori

PY - 2010

Y1 - 2010

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 - asymptotic expansion

KW - Mellin-transform

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

VL - 1264

SP - 100

EP - 113

BT - AIP Conference Proceedings

ER -