A sequence is positive definite if the moment of every nonnegative polynomial which is not identically zero is greater than zero (Widder 1941, p. 132). Here, the moment of a polynomial
with respect to the sequence is defined as
(Widder 1941, p. 102).
This entry contributed by Ronald M. Aarts
More things to try:
Aarts, Ronald M. "Positive Definite Sequence." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PositiveDefiniteSequence.html