The Nevanlinna parametrization and the indeterminate Stieltjes moment problem (Q1364160)

For the probability \(\mu\in{\mathcal M}\) the sequence of moments \(t_n= \int x^nd\mu(x)\) was considered (\({\mathcal M}\) is the set of positive measures on the real axis of all orders and infinite support). A relation was given for the Nevanlinna parametrization describing a one-to-one correspondence between all solutions of the moment problem and the class of Pick functions \(f\). A necessary and sufficient condition was found for a Pick function \(f\) so that the corresponding measure \(\sigma_f\) is supported on the positive axis.