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Complete Convex Function


A function f(x) is completely convex in an open interval (a,b) if it has derivatives of all orders there and if

 (-1)^kf^((2k))(x)>=0

for k=0, 1, 2, ... in that interval (Widder 1941, p. 177). For example, the functions sinx and cosx are completely convex in the intervals (0,pi) and (-pi/2,pi/2) respectively.


See also

Completely Monotonic Function

This entry contributed by Ronald M. Aarts

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References

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

Referenced on Wolfram|Alpha

Complete Convex Function

Cite this as:

Aarts, Ronald M. "Complete Convex Function." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/CompleteConvexFunction.html

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