论文标题
根据$ Q $ -HERMITE-WEBER差异方程式对Zwegers的$μ$ function的概括
A Generalization of Zwegers' $μ$-Function According to the $q$-Hermite-Weber Difference Equation
论文作者
论文摘要
我们引入了Zwegers的$μ$ function的一个参数变形，作为$ q $ - borel的图像和$ q $ -laplace的图像，用于$ q $ -Hermite-weber方程的基本解决方案。我们进一步为我们的广义$ $ $ function提供了一些公式，例如，前向和向后移动，翻译，对称性，新参数的差异方程以及双边$ q $ $ q $ - hyphepermetric表达式。从一个角度来看，连续$ q $ - 赫米特多项式是我们$ $ unction的一些特殊情况，而Zwegers的$μ$ function被视为连续的$ q $ $ q $ -Hermite of'$ -1 $度''。
We introduce a one parameter deformation of the Zwegers' $μ$-function as the image of $q$-Borel and $q$-Laplace transformations of a fundamental solution for the $q$-Hermite-Weber equation. We further give some formulas for our generalized $μ$-function, for example, forward and backward shift, translation, symmetry, a difference equation for the new parameter, and bilateral $q$-hypergeometric expressions. From one point of view, the continuous $q$-Hermite polynomials are some special cases of our $μ$-function, and the Zwegers' $μ$-function is regarded as a continuous $q$-Hermite polynomial of ''$-1$ degree''.
