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arXiv · 1510.00192

A note on a modified Bessel function integral

R. B. Paris
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Abstract

We investigate the integral \[\int_0^\infty \cosh^\mu\!t\,K_\nu(z\cosh t)\,dt \qquad \Re(z)>0,\] where $K$ denotes the modified Bessel function, for non-negative integer values of the parameters $\mu$ and $\nu$. When the integers are of different parity, closed-form expressions are obtained in terms of $z^{-1}e^{-z}$ multiplied by a polynomial in $z^{-1}$ of degree dependent on the sign of $\mu-\nu$.

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R. B. Paris. 2015-10-01. A note on a modified Bessel function integral. https://arxiv.org/abs/1510.00192

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