  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.
