A (slightly more) complicated integral

From: Enrique Aguado (l.e.aguado_at_leeds.ac.uk)
Date: 06/18/04 

Date: Fri, 18 Jun 2004 12:20:09 +0100

Ok, so the previous integral ended up being a piece of cake,
however this one cannot be done in the same way (and it ends up that
this one is the one I really want, isn't it always the same?)

It looks like this:

Int[Int[E^(a Cos[x]+ b Cos[y]+ k Cos[x - y]) {y, -Pi, Pi}],{x, -Pi, Pi}]

Any suggestions anyone?

Many many thanks in advance

Enrique