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arXiv · 1711.06849

Closed form expressions for derivatives of Bessel functions with respect to the order

J. L. González-Santander
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Abstract

We have used recent integral representations of the derivatives of the Bessel functions with respect to the order to obtain closed-form expressions in terms of generalized hypergeometric functions and Meijer-$G$ functions. Also, we have carried out similar calculations for the derivatives of the modified Bessel functions with respect to the order, obtaining closed-form expressions as well. For this purpose, we have obtained integral representations of the derivatives of the modified Bessel functions with respect to the order. As by-products, we have calculated two non-tabulated integrals.

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BibTeXRIS

J. L. González-Santander. 2018-06-03. Closed form expressions for derivatives of Bessel functions with respect to the order. https://doi.org/10.1016/j.jmaa.2018.06.043

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