From q-analytic functions to double q-analytic Hermite binomials and q-traveling waves

International Conference on Quantum Science and Applications 2016

Tumer, Sengul Nalci^1 ; Pashaev, Oktay K.^1

Department of Mathematics, Izmir Institute of Technology, Gulbahce Campus, Urla, Izmir

35430, Turkey^1

关键词: Analytic functions;    Complex argument;    Complex functions;    Hermite;    Hermite polynomials;    Q-analogues;    Traveling wave;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/766/1/012017/pdf
DOI  :  10.1088/1742-6596/766/1/012017

来源: IOP

【 摘 要 】

We extend the concept of q-analytic function in two different directions. First we find expansion of q-binomial in terms of q-Hermite polynomials, analytic in two complex arguments. Based on this representation, we introduce a new class of complex functions of two complex arguments, which we call the double q-analytic functions. As another direction, by the hyperbolic version of q-analytic functions we describe the q-analogue of traveling waves, which is not preserving the shape during evolution. The IVP for corresponding q-wave equation we solved in the q-D'Alembert form.