It is shown that a function f is a generalized Stieltjes function of order $$\lambda >0$$λ>0if and only if $$x^{1-\lambda }(x^{\lambda -1+k}f(x))^{(k)}$$x1-λ(xλ-1+kf(x))(k)is completely monotonic for all $$k\ge 0$$k≥0, ...

In this paper an abstract condition is given yielding universal series defined by sequences a = {aj}∞ j=1 in ∩p>1ℓp but not in ℓ1. We obtain a unification of some known results related to approximation by translates of ...