Working Paper Article Version 1 This version is not peer-reviewed

Asymptotics and Confluence for Some Linear q-Difference-Differential Cauchy Problem

Version 1 : Received: 22 February 2021 / Approved: 23 February 2021 / Online: 23 February 2021 (11:02:00 CET)

How to cite: Malek, S. Asymptotics and Confluence for Some Linear q-Difference-Differential Cauchy Problem. Preprints 2021, 2021020509 Malek, S. Asymptotics and Confluence for Some Linear q-Difference-Differential Cauchy Problem. Preprints 2021, 2021020509

Abstract

A linear Cauchy problem with polynomial coefficients wich combines q-difference operators for q>1 and differential operators of irregular type is examined. A finite set of sectorial holomorphic solutions w.r.t the complex time is constructed by means of classical Laplace transforms. These functions share a common asymptotic expansion in the time variable which turns out to carry a double layers structure which couples q-Gevrey and Gevrey bounds. In the last part of the work, the problem of confluence of these solutions as q tends to 1 is investigated.

Keywords

asymptotic expansion; confluence; formal power series; partial differential equation; q-difference equation

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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