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Let a_n>=0 and suppose sum_(n=1)^inftya_ne^(-an)∼1/a as a->0^+. Then sum_(n<=x)a_n∼x as x->infty. This theorem is a step in the proof of the prime number theorem, but has ...

The hat is a caret-shaped symbol commonly placed on top of variables to give them special meaning. The symbol x^^ is voiced "x-hat" (or sometimes as "x-roof") in mathematics, ...

An integer n>1 is said to be highly cototient if the equation x-phi(x)=n has more solutions than the equations x-phi(x)=k for all 1<k<n, where phi is the totient function. ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), define the Hilbert function of M as the map ...

A synonym for analytic function, regular function, differentiable function, complex differentiable function, and holomorphic map (Krantz 1999, p. 16). The word derives from ...

An indirectly conformal mapping, sometimes called an anticonformal mapping, is a mapping that reverses all angles, whereas an isogonal mapping can reverse some angles and ...

The (lower) irredundance number ir(G) of a graph G is the minimum size of a maximal irredundant set of vertices in G. The upper irredundance number is defined as the maximum ...

The jinc function is defined as jinc(x)=(J_1(x))/x, (1) where J_1(x) is a Bessel function of the first kind, and satisfies lim_(x->0)jinc(x)=1/2. The derivative of the jinc ...

An algorithm for finding a graph's spanning tree of minimum length. It sorts the edges of a graph in order of increasing cost and then repeatedly adds edges that bridge ...

The Landau-Mignotte bound, also known as the Mignotte bound, is used in univariate polynomial factorization to determine the number of Hensel lifting steps needed. It gives ...