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A number which is simultaneously a heptagonal number H_n and square number S_m. Such numbers exist when 1/2n(5n-3)=m^2. (1) Completing the square and rearranging gives ...

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 term "isomorphic" means "having the same form" and is used in many branches of mathematics to identify mathematical objects which have the same structural properties. ...

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 ordinary differential equation (1) (Byerly 1959, p. 255). The solution is denoted E_m^p(x) and is known as an ellipsoidal harmonic of the first kind, or Lamé function. ...