Thread: Integral involving expoential - does it have a name?

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.

Originally Posted by astronomerroyal

I have found solutions for integer

What if ?

Originally Posted by chiph588@

What if ?

? 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.).