On functions K and E generated by a sequence of moments

For a class of functions γ analytic in the angle {s:|arg(s)|<α0} with π2<α0<π, we describe the asymptotic behaviour of the entire function E(z)=∑n≥0znγ(n+1)and of the analytic function K(z)=12πi∫c−i∞c+i∞z−sγ(s)dsthat solves the moment problem ∫0∞tnK(t)dt=γ(n+1),n≥0.