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The regularized beta function is defined by I(z;a,b)=(B(z;a,b))/(B(a,b)), where B(z;a,b) is the incomplete beta function and B(a,b) is the (complete) beta function. The ...

The regularized gamma functions are defined by P(a,z) = (gamma(a,z))/(Gamma(a)) (1) Q(a,z) = (Gamma(a,z))/(Gamma(a)), (2) where gamma(a,z) and Gamma(a,z) are incomplete gamma ...

Resolution is a widely used word with many different meanings. It can refer to resolution of equations, resolution of singularities (in algebraic geometry), resolution of ...

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 ...

The Riemann sphere, also called the extended complex plane, is a one-dimensional complex manifold C^* (C-star) which is the one-point compactification of the complex numbers ...

A ruled surface is called a right conoid if it can be generated by moving a straight line intersecting a fixed straight line such that the lines are always perpendicular ...

Given a commutative unit ring R, and an R-module M, a sequence {x_1,...,x_n} of elements of R is called a regular sequence for M (or an M-sequence for short), if, for all ...

One of the three standard tori given by the parametric equations x = (c+acosv)cosu (1) y = (c+acosv)sinu (2) z = asinv (3) with c>a. This is the torus which is generally ...

Let f be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then if f(a)=f(b), then there is at least one point c in (a,b) where f^'(c)=0. ...

If the sides of a triangle are divided in the ratios lambda:1, mu:1, and nu:1, the cevians form a central triangle whose area is ...