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In mathematics, **Hardy's theorem** is a result in complex analysis describing the behavior of holomorphic functions.

Let be a holomorphic function on the open ball centered at zero and radius in the complex plane, and assume that is not a constant function. If one defines

for then this function is strictly increasing and is a convex function of .

- John B. Conway. (1978)
*Functions of One Complex Variable I*. Springer-Verlag, New York, New York.

*This article incorporates material from Hardy's theorem on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.*