The Early History of the Moment Problem

In the present study it is discussed how the moment problem naturally arose within Stieltjes' creation of the analytical theory of continued fractions. Further it is shown how the moment problem in the work of Hamburger came to be regarded as an important problem in its own right. From then on it moved away from its origin into other fields of mathematics—complex function theory and functional analysis—in the work of Nevanlinna and M. Riesz respectively. In the end it was made completely independent from continued fractions.