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The complementary Bell numbers, also called the Uppuluri-Carpenter numbers, B^~_n=sum_(k=0)^n(-1)^kS(n,k) (1) where S(n,k) is a Stirling number of the second kind, are ...

A reduction system is called confluent (or globally confluent) if, for all x, u, and w such that x->_*u and x->_*w, there exists a z such that u->_*z and w->_*z. A reduction ...

The Coulomb wave function is a special case of the confluent hypergeometric function of the first kind. It gives the solution to the radial Schrödinger equation in the ...

A general system of fourth-order curvilinear coordinates based on the cyclide in which Laplace's equation is separable (either simply separable or R-separable). Bôcher (1894) ...

An evolute is the locus of centers of curvature (the envelope) of a plane curve's normals. The original curve is then said to be the involute of its evolute. Given a plane ...

A method for solving an equation by approximating continuous quantities as a set of quantities at discrete points, often regularly spaced into a so-called grid or mesh. ...

The hyperbolic cosecant is defined as cschz=1/(sinhz)=2/(e^z-e^(-z)). (1) It is implemented in the Wolfram Language as Csch[z]. It is related to the hyperbolic cotangent ...

The hyperbolic octahedron is a hyperbolic version of the Euclidean octahedron, which is a special case of the astroidal ellipsoid with a=b=c=1. It is given by the parametric ...

An Archimedean spiral with polar equation r=a/theta. (1) The hyperbolic spiral, also called the inverse spiral (Whittaker 1944, p. 83), originated with Pierre Varignon in ...

The Jordan matrix decomposition is the decomposition of a square matrix M into the form M=SJS^(-1), (1) where M and J are similar matrices, J is a matrix of Jordan canonical ...