I am wondering whether the following integral

$$ Y = \int_{x_0}^{x_1} \exp{\left(a\cos x+b\sin x\right)}\,dx,$$

has a known closed form for given $a,b,x_0$ and $x_1$.

Since the exponential of the periodic function $a\cos x+b\sin x$ is also periodic, I know that this integral can be computed under a period, and the solution in terms of a modified Bessel function can be found here.

But, what about for general integral limits?

Thanks for any hint!

  • 1
    $\begingroup$ See here. $\endgroup$ – Count Iblis Jul 21 '18 at 16:39
  • $\begingroup$ Be more specific, please. $\endgroup$ – A. Pongrácz Jul 21 '18 at 18:06
  • $\begingroup$ @A.Pongrácz, I did not get your point. $\endgroup$ – Alex Silva Jul 21 '18 at 18:25
  • $\begingroup$ @CountIblis, Thanks for the paper. :) $\endgroup$ – Alex Silva Jul 22 '18 at 18:35

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