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Ein(z) = int_0^z((1-e^(-t))dt)/t (1) = E_1(z)+lnz+gamma, (2) where gamma is the Euler-Mascheroni constant and E_1 is the En-function with n=1.

Let V(r) be the volume of a ball of radius r in a complete n-dimensional Riemannian manifold with Ricci curvature tensor >=(n-1)kappa. Then V(r)<=V_kappa(r), where V_kappa is ...

The trilinear coordinates alpha:beta:gamma of a point P relative to a reference triangle are proportional to the directed distances a^':b^':c^' from P to the side lines of ...

Let U subset= C be a domain, and let f be an analytic function on U. Then if there is a point z_0 in U such that |f(z_0)|>=|f(z)| for all z in U, then f is constant. The ...

A geometric series sum_(k)a_k is a series for which the ratio of each two consecutive terms a_(k+1)/a_k is a constant function of the summation index k. The more general case ...

A set n distinct numbers taken from the interval [1,n^2] form a magic series if their sum is the nth magic constant M_n=1/2n(n^2+1) (Kraitchik 1942, p. 143). If the sum of ...

Defining p_0=2, p_n as the nth odd prime, and the nth prime gap as g_n=p_(n+1)-p_n, then the Cramér-Granville conjecture states that g_n<M(lnp_n)^2 for some constant M>1.

A curvilinear polygon built up of circular arcs. The Reuleaux polygon is a generalization of the Reuleaux triangle and, for an odd number of sides, is a curve of constant ...

A curve in two dimensions on which the value of a function f(x,y) is a constant. Other synonymous terms are equipotential curve, isarithm, and isopleth. A plot of several ...

A chord which is a normal at each end. A centrosymmetric set K subset R^d has d double normals through the center (Croft et al. 1991). For a curve of constant width, all ...