I am trying to sum the following expression:
(Cos[(2 π m)/N]^2 Cos[(2 π n)/ N])/(2 (Cos[(2 m π)/N] - Cos[(2 n π)/N]))
(N+1)/2 excluding the term
m=n. I split this sum into two: the first from
n-1, and the second from
I run into two problems: the first series just does not evaluate (Mathematica returns the expression). However when I plot it plugging in some values for
N always greater than
n), I find the function to be well behaved in the interval.
The second series from
(N+1)/2 does sum, but it evaluates to complicated
QPolygamma functions, and
FullSimplify doesn't help. Any help would be appreciated!