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I am a physicist who needs to evaluate the following (divergent at the origin) integral involving the modified Bessel functions of the first and second kinds

$$I = \int_0^{\infty} \frac{\cos(ax)}{x} I_0(bx) K_1(cx) \mathrm{d}x$$

where $a, b, c$ are real and positive numbers.

It does not appear in Gradshteyn and Ryzhik, and it is not known by Mathematica.

Can any mathematicians suggest a method or trick to evaluate this integral exactly or approximately?

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  • $\begingroup$ the value of $I$ is $\infty$, what is there to evaluate or approximate? $\endgroup$ – Carlo Beenakker Aug 29 '15 at 12:47
  • $\begingroup$ Are you intending to integrate from 0 to infinity? As the above commenter pointed out, there's no way that integral can be evaluated to anything but infinity. $\endgroup$ – Zorgoth Dec 8 '15 at 23:13

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