High-order derivatives of the Bessel functions with an application

Abstract

We determine the asymptotic behaviour of the $n$th derivatives of the Bessel functions $J_{\nu }(a)$ and $K_{\nu }(a)$, where $a$ is a fixed positive quantity, as $n\to \infty$. These results are applied to the asymptotic evaluation of two incomplete Laplace transforms of these Bessel functions on the interval $[0,a]$ as the transform variable $x\to +\infty$. Similar evaluation of the integrals involving the Bessel functions $Y_{\nu }(t)$ and $I_{\nu }(t)$ is briefly mentioned.

12 pages, 0 figures

References in corpus (1)

• Inequalities for modified Bessel functions and their integrals