High-order derivatives of the Bessel functions with an application

R B Paris

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arXiv · 1905.04673

High-order derivatives of the Bessel functions with an application

R B Paris

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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.

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R B Paris. 2019-05-12. High-order derivatives of the Bessel functions with an application. https://arxiv.org/abs/1905.04673

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