Witryna23 lut 2016 · $\begingroup$ @YulInn: The most natural and elemenary definition of the natural logarithm---or its inverse, the exponential---is via calculus, or at least as a limit. … Witryna13 maj 2024 · 1 Introduction. An overpartition of n is a non-increasing sequence of natural numbers whose sum is n in which the first occurrence of a number may be …

Logarithmically concave function - Wikipedia

A logarithmically convex function f is a convex function since it is the composite of the increasing convex function $${\displaystyle \exp }$$ and the function $${\displaystyle \log \circ f}$$, which is by definition convex. However, being logarithmically convex is a strictly stronger property than … Zobacz więcej In mathematics, a function f is logarithmically convex or superconvex if $${\displaystyle {\log }\circ f}$$, the composition of the logarithm with f, is itself a convex function. Zobacz więcej • $${\displaystyle f(x)=\exp( x ^{p})}$$ is logarithmically convex when $${\displaystyle p\geq 1}$$ and strictly logarithmically convex when • Zobacz więcej Let X be a convex subset of a real vector space, and let f : X → R be a function taking non-negative values. Then f is: • Logarithmically convex if $${\displaystyle {\log }\circ f}$$ is … Zobacz więcej • Logarithmically concave function Zobacz więcej In convex analysis, a non-negative function f : R → R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it satisfies the inequality for all x,y ∈ dom f and 0 < θ < 1. If f is strictly positive, this is equivalent to saying that the logarithm of the function, log ∘ f, is concave; that is, for all x,y ∈ dom f and 0 < θ < 1. tax office wood county

On the log-convexity of combinatorial sequences - ScienceDirect

Witryna14 lip 2016 · A body E is completely embedded within a convex body G. A line segment is generated by a measure depending only on E or on both E and G . This line segment is then projected to the surface of G in one or both directions. WitrynaLet [A n,k] n,k ⩾0 be an infinite lower triangular array satisfying the recurrencefor n ⩾ 1 and k ⩾ 0, where A 0,0 = 1, A 0, k = A k,–1 = 0 for k > 0. We present some criteria for the log-concavity of rows and strong q-log-convexity of generating functions of rows.Our results can be applied to many well-known triangular arrays, such as the Pascal … Witryna27 mar 2015 · The graph of convex function is : In a book it is written that g ( x) = log x is strictly convex function. So i searched for graph of g ( x) = log x and found that. Though it has been said that g ( x) = log x is strictly convex function, comparing these two graph it seems to me g ( x) = log x is concave function . Where am i doing mistake ? tax office winnie tx