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Absolutely Monotonic Function

A function f(x) is absolutely monotonic in the interval a<x<b if it has nonnegative derivatives of all orders in the region, i.e.,

f^((k))(x)>=0
(1)

for a<x<b and k=0, 1, 2, .... For example, the functions

f(x)=-ln(-x) (-1<=x<0)
(2)

and

f(x)=sin^(-1)x (0<=x<=1)
(3)

are absolutely monotonic functions (Widder 1941).

This entry contributed by Ronald M. Aarts

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References

Widder, D. V. Ch. 4 in The Laplace Transform. Princeton, NJ: Princeton University Press, 1941.

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Absolutely Monotonic Function

Cite this as:

Aarts, Ronald M. "Absolutely Monotonic Function." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/AbsolutelyMonotonicFunction.html

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