A continuation of the Hankel vector approach on the general rational interpolation problem (GRIP) given by \textit{G. N. Chen}, \textit{B. Zhao} and \textit{H. Zhang} [Linear Algebra Appl. 244, 165-201 (1996; Zbl 0857.93049)] was presented. This approach was extended to the Nevanlinna-Pick (NP) interpolation problem with multiple nodes in the class \({\mathcal N}\) of Nevanlinna functions, which can be considered as a GRIP with certain symmetries. A connection between the NP problem and the problems of the power moment was established. The power moment problem is equivalent to the problem of finding functions which belong to \({\mathcal N}\) with a given asymptotic expansion criteria for the NP problem to be solvable, and to be determinate or indeterminate.