论文标题
广义的Lerche-Newberger公式
A Generalized Lerche-Newberger Formula
论文作者
论文摘要
Lerche-Newberger公式简化了Bessel函数的谐波总和，并在等离子体物理和频率调制量子系统中进行了应用。在本文中，我们严格证明公式并将经典结果扩展到单个变量Bessel函数的多维扩展家族，称为广义Bessel函数。由于这些功能的普遍定义不适合任意复杂顺序，因此我们使用称为广义愤怒函数的辅助功能家族，并表明单个可变性结果在多个维度上符合一定的参数选择。我们结论将这些结果应用于物理系统。
The Lerche-Newberger formula simplifies harmonic sums of Bessel functions and has seen application in plasma physics and frequency modulated quantum systems. In this paper, we rigorously prove the formula and extend the classical result to a family of multi-dimensional extensions of the single variable Bessel functions called generalized Bessel functions. Since prevailing definitions of these functions do not accommodate arbitrary complex order, we use an auxiliary family of functions called generalized Anger functions and show that the single-variable result holds in multiple dimensions for a certain selection of parameters. We conclude by applying these results to physical systems.
