I know most trig related problems belong in the trig section, but I'm pretty sure this one is more number theory related.
Does anyone know an identity for the following:
(sigma[arctan((2x)/(2n+1))], n=1, n=infinity)-x(zeta(1)). x is greater than one and real.
I've seen a few identities for infinite summation with the inverse tangent, but nothing like this. I know it converges because of the integral test, just not what it converges to.
Any help at all would be much appreciated.
I cannot find one, but maybe if someone could use one of these to solve it:
Table of Infinite Products Infinite Sums Infinite Series Elliptic Theta