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The moment of inertia with respect to a given axis of a solid body with density rho(r) is defined by the volume integral I=intrho(r)r__|_^2dV, (1) where r__|_ is the ...

A set A of integers is said to be one-one reducible to a set B (A<<_1B) if there is a one-one recursive function f such that for every x, x in A=>f(x) in B (1) and f(x) in ...

Saalschütz's theorem is the generalized hypergeometric function identity _3F_2[a,b,-n; c,1+a+b-c-n;1]=((c-a)_n(c-b)_n)/((c)_n(c-a-b)_n) (1) which holds for n a nonnegative ...

A topological space, also called an abstract topological space, is a set X together with a collection of open subsets T that satisfies the four conditions: 1. The empty set ...

A uniform distribution, sometimes also known as a rectangular distribution, is a distribution that has constant probability. The probability density function and cumulative ...

A space-filling polyhedron is a polyhedron which can be used to generate a tessellation of space. Although even Aristotle himself proclaimed in his work On the Heavens that ...

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 ...

A polynomial A_n(x;a) given by the associated Sheffer sequence with f(t)=te^(at), (1) given by A_n(x;a)=x(x-an)^(n-1). (2) The generating function is ...

The term "aliquot divisor" is commonly used to mean two distinct but related things. The first definition is a number that divides another exactly. For instance, 1, 2, 3, and ...

Another "beta function" defined in terms of an integral is the "exponential" beta function, given by beta_n(z) = int_(-1)^1t^ne^(-zt)dt (1) = ...