ABSTRACT
The first appearance of the Stieltjes transform was reported in Stieltjes' paper https://www.w3.org/1998/Math/MathML"> [ 219 ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780138752859/46b98bf4-f43d-4c1b-bad9-d831e2ef6414/content/eq3376.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> on continued fractions. The Dutch mathematician T.J. Stieltjes made several notable contributions in mathematics; his ideas, together with those of Lebesgue have led to one of the well-known integrals of the twentieth century, the Lebesgue-Stieltjes integral. The Stieltjes transform arose also in connection with Stieltjes' moment problem for a semi-infinite interval.
