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A formula for the Bell polynomial and Bell numbers. The general formula states that B_n(x)=e^(-x)sum_(k=0)^infty(k^n)/(k!)x^k, (1) where B_n(x) is a Bell polynomial (Roman ...

Sphere tetrahedron picking is the selection of quadruples of of points corresponding to vertices of a tetrahedron with vertices on the surface of a sphere. n random ...

A leaf of an unrooted tree is a node of vertex degree 1. Note that for a rooted or planted tree, the root vertex is generally not considered a leaf node, whereas all other ...

The interval (generally, the smallest interval) over which the values of a periodic function recur. Functions may have one or more periods over time and in space.

The symbol tau (the lower case Greek letter tau) has many common uses in mathematics, as summarized in the following table. 1. tau(n) is an alternate notation for the divisor ...

Probability and Statistics

The Jacobi theta functions are the elliptic analogs of the exponential function, and may be used to express the Jacobi elliptic functions. The theta functions are ...

The antilaplacian of u with respect to x is a function whose Laplacian with respect to x equals u. The antilaplacian is never unique.

The process of taking the complement of a set or truth function. In the latter case, complementation is equivalent to the NOT operation.

The function f(beta,z)|->z^((1+cosbeta+isinbeta)/2), illustrated above for beta=0.4.