TOPICS
Search

Positive Definite Sequence

A sequence {mu_n}_(n=0)^infty 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

P_n(x)=sum_(m=0)^na_mx^m

with respect to the sequence {mu_n}_(n=0)^infty is defined as

M(P_n(x))=sum_(m=0)^na_mmu_m

(Widder 1941, p. 102).

This entry contributed by Ronald M. Aarts

Explore with Wolfram|Alpha

References

Widder, D. V. The Laplace Transform. Princeton, NJ: Princeton University Press, 1941.

Referenced on Wolfram|Alpha

Positive Definite Sequence

Cite this as:

Aarts, Ronald M. "Positive Definite Sequence." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PositiveDefiniteSequence.html

Subject classifications