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?

  • $\begingroup$ the value of $I$ is $\infty$, what is there to evaluate or approximate? $\endgroup$ Commented Aug 29, 2015 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
    Commented Dec 8, 2015 at 23:13


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.