Logarithmically convex function
- Logarithmically convex function
In mathematics, a function defined on an convex subset of a real vector space and taking positive values is said to be logarithmically convex if is a convex function of .
It is easy to see that a logarithmically convex function is a convex function, but the converse is not true. For example is a convex function, but is not a convex function and thus is not logarithmically convex. On the other hand, is logarithmically convex since is convex. A less trivial example of a logarithmically convex function is the gamma function, if restricted to the positive reals (see also the Bohr–Mollerup theorem).
References
* John B. Conway. "Functions of One Complex Variable I", second edition. Springer-Verlag, 1995. ISBN 0-387-90328-3. ----
*planetmath|id=5664|title=logarithmically convex function
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