Hankel vector moment sequences and the non-tangential regularity at infinity of two variable pick functions

A Pick function of d variables is a holomorphic map from Π^d to Π, where Π is the upper halfplane. Some Pick functio∑ of one variable havean asymptotic expansion at infinity, a power series with real numbers ρ_n that gives an asymptotic expansion on non-tangential approach regions to infinity. In 1921 H. Hamburger characterized which sequences {ρ_n} can occur. We give an extension of Hamburger's results to Pick functions of two variables.