is defined as
You can find that
If your prof wants you to evaluate those series then I don't know (I used Maple). Well I don't have the time... or both.
I don't think so because it is
because the first term is 0 not 1 we must integrate from 1 to infinity not 0 to infinity. But I may be mistaking.
Here are the 10 first terms
(I'm assuming you know how to go about diagonalizing a matrix; if not, there is an article on Wikipedia:
Diagonalizable matrix - Wikipedia, the free encyclopedia.)