A function 
is absolutely monotonic in the interval 
if it has nonnegative derivatives of all orders
in the region, i.e.,
 |
(1)
|
for 
and 
,
1, 2, .... For example, the functions
 |
(2)
|
and
 |
(3)
|
are absolutely monotonic functions (Widder 1941).
See also
Absolutely Monotonic
Sequence
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.Referenced
on Wolfram|Alpha
Absolutely Monotonic Function
Cite this as:
Aarts, Ronald M. "Absolutely Monotonic Function." From MathWorld--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/AbsolutelyMonotonicFunction.html
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