This expression shows up when deriving a formula for antenna radiation [Wu/Storer/etc]. Is it exact or just an approximation?

$$\int_0^{\pi/2} K_0 ( 2 \lambda \sin \theta) d \theta = \pi/2 K_0 (\lambda) I_0 (\lambda)$$

If I plot both expressions as a function of $\lambda$, then the two curves do indeed seem to overlay very well.

Thanks, John p.s. Hm, maybe a special case of this question: A definite integral on a circle with Bessel functions


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