再论Airy积分与Bessel函数的关系
On the relation between Airy integral and Bessel functions revisited
摘要：
Airy积分和Bessel函数对于描述相对论带电粒子在同步加速器中运动以及在周期性宏观和微观结构中产生的不同类型辐射的光谱分布具有重要意义。Airy积分与修正Bessel函数之间关系的简单证明对于不精通纯数学的辐射物理学家来说是非常重要的。本文讨论了Nicholson提出的一个古老的证明，并提出了另一个基于复常数Bessel微分方程的Bowman变换的简单证明。
英文摘要：
The Airy integral and Bessel functions are of significant in mathematical description of spectral distribution of different types of radiation produced by relativistic charged particles moving in synchrotron and in periodical macro- and micro-structures. A simple proof of the relation between Airy integral and modified Bessel function is of most important for radiation physicists, who are not expert in pure mathematics. In this paper we discuss an old proof proposed by Nicholson, and suggest another simple one based on the Bowman transformation of Bessel differential equation with a complex constant.
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