I'm working with this simple little integral,
,
and was wondering if it had a name. It seems so basic that I imagine there's a lot of literature written about it - I would like to know more about it.
An observation: If the limits were 0 and infinity the solution would be related to gamma functions.
I have found solutions for integer (integrate by parts once, then note a recursion relation). Then general solutions can be written down; one for even and one for odd .
e.g. for odd
I think that's correct - I'm just getting the feeling that it must have been solved a million times before...
Any thoughts?
Thanks in advance,
Tom.
? Error functions.
For non-zero, positive integer the integral reminds one of the moment equation for the gaussian. This is just one of the reasons I believe that huge tomes have already been written on this particular integral. However, I'm not finding the tomes (via google, wikipedia, colleagues etc.).