| Log-convex |
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| CATEGORIES ABOUT LOGARITHMICALLY CONVEX FUNCTION | |
| real analysis | |
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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 Bohr-Mollerup Theorem .) The definition is easily extended to functions where still we have , in the obvious way. Such a function is logarithmically convex if it is logarithmically convex on all intervals . |
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