The Rocky Mountain journal of mathematics vol:33 issue:2 pages:609-627
2001: A Mathematical Odyssey location:Mesa State College, Grand Junction, CO date:6-10 August 2001
The constructive solution of the strong Stieltjes moment problem can be linked with positive Perron-Caratheodory continued fractions (PC-fractions) which are contradictions of positive Thron continued fractions (T-fractions). Their approximants are two-point Pade approximants for a related function. The multi-point moment problem similarly leads to positive multi-point Pade continued fractions (MP-fraction) and positive extended multi-point Pade continued fractions (EMP-fraction) whose approximants are multi-point Pade approximants. These relationships are explored also in the situation where the positivity condition is dropped.