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A generalization of Student's t-distribution known as the noncentral Student's t-distribution is given by (1) where Gamma(z) is the gamma function and _1F_1(a;b;z) is a ...

Define the harmonic mean of the divisors of n H(n)=(sigma_0(n))/(sum_(d|n)1/d), where sigma_0(n) is the divisor function (the number of divisors of n). For n=1, 2, ..., the ...

Given a regular pentagon of unit area, mean triangle area of a triangle picked at random inside it is given by the n=5 case of polygon triangle picking, A^_ = ...

The symbol +/- is used to denote a quantity which should be both added and subtracted, as in a+/-b. The symbol can be used to denote a range of uncertainty, or to denote a ...

The term "quotient" is most commonly used to refer to the ratio q=r/s of two quantities r and s, where s!=0. Less commonly, the term quotient is also used to mean the integer ...

If f:D->Y is a map (a.k.a. function, transformation, etc.) over a domain D, then the range of f, also called the image of D under f, is defined as the set of all values that ...

Let P and U be points, neither of which lies on a sideline of DeltaABC, given in barycentric coordinates by P=p:q:r and U=u:v:w. The P-reciprocal conjugate of U is then the ...

The Robbins constant is the mean line segment length, i.e., the expected distance between two points chosen at random in cube line picking, namely Delta(3) = (1) = (2) = ...

Two figures are said to be similar when all corresponding angles are equal and all distances are increased (or decreased) in the same ratio, called the ratio of magnification ...

Tetrahedron picking is the process of picking tetrahedra at random within a given shape in 3 or higher dimensions. The most natural definition of a random tetrahedron is one ...