Search Results for ""

Lauricella functions are generalizations of the Gauss hypergeometric functions to multiple variables. Four such generalizations were investigated by Lauricella (1893), and ...

Spherical coordinates, also called spherical polar coordinates (Walton 1967, Arfken 1985), are a system of curvilinear coordinates that are natural for describing positions ...

An nth-rank tensor in m-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules. Each index of a tensor ranges ...

Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A ...

There are two kinds of Bell polynomials. A Bell polynomial B_n(x), also called an exponential polynomial and denoted phi_n(x) (Bell 1934, Roman 1984, pp. 63-67) is a ...

Newton's method for finding roots of a complex polynomial f entails iterating the function z-[f(z)/f^'(z)], which can be viewed as applying the Euler backward method with ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

The Whittaker functions arise as solutions to the Whittaker differential equation. The linearly independent solutions to this equation are M_(k,m)(z) = ...

A theorem which effectively describes how lengths, areas, volumes, and generalized n-dimensional volumes (contents) are distorted by differentiable functions. In particular, ...

A discrete function A(n,k) is called closed form (or sometimes "hypergeometric") in two variables if the ratios A(n+1,k)/A(n,k) and A(n,k+1)/A(n,k) are both rational ...