  We consider the powers of leading order eigenvalue of the
Balitsky-Fadin-Kuraev-Lipatov~(BFKL) equation at zero conformal spin. Using
reflection identities of harmonic sums we demonstrate how involved generalized
polygamma functions are introduced by pole separation of a rather simple
digamma function. This generates higher weight generalized polygamma functions
at any given order of perturbative expansion. As a byproduct of our analysis we
develop a general technique for calculating powers of the real part of digamma
function in a pole separated form.

High Energy Physics - Theory