Bessel integral with a square-root trigonometric argument?

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I am seeking a closed form solution to the following integral:

$\int_{-\pi}^{\pi} I_0(b \sqrt{1 - a^2 cos^2\phi}) d\phi$

where $I_0(x)$ is the modified Bessel function of the first kind of order 0.

I have seen a similar question asked here, but I'm not sure how much it helps me.