I am trying to evaluate a infinite series: $$ 2 \sum _{l=1}^{\infty } \Re\left(n^{\frac{2 i \pi l}{\log (q)}} \Gamma \left(\alpha -\frac{2 i l \pi }{\log (q)}\right)\right) $$ With the code:
delta[\[Alpha]_, q_, n_] =
2 Sum[Re[Gamma[\[Alpha] - I 2 l \[Pi]/Log[q]] Exp[
I 2 l \[Pi] Log[n]/Log[q]]], {l, 1, Infinity}]
delta[1,10,10]
N[%]
But Mathematica complaints:
NSum::nsnum: Summand (or its derivative) ((0. +3.14159 I) 2.^(1. +(0. +2.72875 I) l) 5.^((0. +2.72875 I) l) Gamma[1. -(0. +2.72875 I) l]-(0. +1.36438 I) 2.^(1. +(>) l) > Gamma[1. -(0. +>) l] PolyGamma[0.,1. -(0. +2.72875 I) l]) > is not numerical at point l = 16.
Please help me to evaluate it or explain the problem, Thanks!