@Semiclassical Unfortunate, it happens sometimes. Consider self-answering if it goes, perhaps. Ah, I just saw the integral, but unfortunately I don't see immediately that it is the Laplace transform of J_{nu} (50 seconds later) OH, now I see what you mean more clearly, though I'd want to work it out. Yeah, Erdelyi would probably have something on it, speaking of which, I should probably add Erdelyi to my book collection.
@user2661923 I voted to undelete the question. Of course, you could as well, if you think it's worth it. Also, the question was automatically deleted by the Community user, which I think only happens to closed questions with no upvotes. So, if you think a question is interesting enough to answer and maintain, then it's probably worth your upvote as well.
@user2661923 (1) When you make a request involving a question which you have either asked or answered, please disclose this fact. (2) The question is a problem statement question, hence was appropriately deleted. (3) I don't see how it is a "highly relevant Covid question." It is, in fact, a very standard exercise from an intro stats class (I've put something similar on most stats finals I've written).