Abramowitz and Stegun is a classic reference book which contains all sorts of information about special functions and their integrals. If you’ve ever needed to reference something on the road and don’t have your copy with you, you will be happy to learn that the book is accessible online.
I happened across this by pure dumb luck while looking for some sort of obscure Bessel function integral some time ago…
Good to know! I figure there must have been some class I should have taken which would have explained Bessel functions, but as it is, they just show up when a problem is on the edge of analytical tractability, and I manage to get by with the incidental knowledge about such things I picked up along the way.
Blake: Bessels are one of those things that are hard to teach, simply because their usefulness doesn’t become apparent until one has a real need to use them. Being in optics, they’ve become (almost) as comfortable to me as sine and cosine functions. The crucial difference is that I can usually figure out useful trig relations without looking them up, whereas for Bessel functions I can only remember that there is a useful Bessel relationship, and then I have to look up the details.
dammit, I am only informed after I have bought a copy.
I got mine because I was coding (in c) some obscure functions. It has loads of choice of series, so I could pick one that I could make computationally efficient. Then it has tables, so I could make sure I got it right.
Colonal: I would still think it’s useful to have a hard copy on hand; I certainly find it easier to flip through the book than on the computer. It never hurts to have online access, though, for those times when one is away from the office copy…
BTW, there are pdf versions as well. Search for “Abramowitz and Stegun pdf”.
Trey: Thanks for the info! That will be one more massive pdf to overload my laptop harddrive with…
I used to search through the (accurately termed) massive pdf of A&S on my laptop; however this web version with hyperlinks is much more easier to search for useful stuff. Thanks for the info!