asymptotics of $J_{iu} (ia)$ for a Bessel function

Let $J_{iu}(ia)$ be the Bessel function of imaginary order. ($a$ is a real number (positive or negative) and $u$ is also real.)

In the limit $u \to \infty$ how does the function $J_{iu} (ia)$ behave?

How about $J_{iu}(a)$?

Thanks.

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dx.doi.org/10.1137/0521055 may help. – Eckhard Dec 17 '12 at 9:24