A function 
is logarithmically concave on the interval ![[a,b]](/images/equations/LogarithmicallyConcaveFunction/Inline2.svg)
if 
and 
is concave on ![[a,b]](/images/equations/LogarithmicallyConcaveFunction/Inline5.svg)
.
The definition can also be extended to 
functions (Dharmadhikari and Joag-Dev 1988,
p. 18).
Logarithmically Concave Function
See also
Concave Function, Logarithmically Convex FunctionExplore with Wolfram|Alpha
References
Dharmadhikari, S. and Joag-Dev, K. Unimodality, Convexity, and Applications. Boston, MA: Academic Press, 1988.Referenced on Wolfram|Alpha
Logarithmically Concave FunctionCite this as:
Weisstein, Eric W. "Logarithmically Concave Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LogarithmicallyConcaveFunction.html