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Hamburger Moment Problem


A necessary and sufficient condition that there should exist at least one nondecreasing function alpha(t) such that

 mu_n=int_(-infty)^inftyt^ndalpha(t)

for n=0, 1, 2, ..., with all the integrals converging, is that sequence {mu_n}_0^infty is positive definite (Widder 1941, p. 129).


This entry contributed by Ronald M. Aarts

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References

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

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Hamburger Moment Problem

Cite this as:

Aarts, Ronald M. "Hamburger Moment Problem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/HamburgerMomentProblem.html

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