Completely Monotonic Function

A completely monotonic function is a function f(x) such that


for n=0, 1, 2, .... Such functions occur in areas such as probability theory (Feller 1971), numerical analysis, and elasticity (Ismail et al. 1986).

See also

Complete Convex Function, Monotonic Function

This entry contributed by Ronald M. Aarts

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Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 2, 3rd ed. New York: Wiley, 1971.Ismail, M. E. H.; Lorch, L.; and Muldon, M. E. "Completely Monotonic Functions Associated with the Gamma Function and Its q-Analogues." J. Math. Anal. Appl. 116, 1-9, 1986.Widder, D. V. The Laplace Transform. Princeton, NJ: Princeton University Press, 1941.

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Completely Monotonic Function

Cite this as:

Aarts, Ronald M. "Completely Monotonic Function." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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