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For any algebraic number x of degree n>2, a rational approximation p/q to x must satisfy |x-p/q|>1/(q^n) for sufficiently large q. Writing r=n leads to the definition of the ...

The Mercator series, also called the Newton-Mercator series (Havil 2003, p. 33), is the Taylor series for the natural logarithm ln(1+x) = sum_(k=1)^(infty)((-1)^(k+1))/kx^k ...

For any M, there exists a t^' such that the sequence n^2+t^', where n=1, 2, ... contains at least M primes.

Consider a line segment of length 1, and pick a point x at random between [0,1]. This point x divides the line into line segments of length x and 1-x. If a set of points are ...

An arithmetic progression of primes is a set of primes of the form p_1+kd for fixed p_1 and d and consecutive k, i.e., {p_1,p_1+d,p_1+2d,...}. For example, 199, 409, 619, ...

Kurtosis is defined as a normalized form of the fourth central moment mu_4 of a distribution. There are several flavors of kurtosis, the most commonly encountered variety of ...

Let the probabilities of various classes in a distribution be p_1, p_2, ..., p_k, with observed frequencies m_1, m_2, ..., m_k. The quantity ...

Maximum likelihood, also called the maximum likelihood method, is the procedure of finding the value of one or more parameters for a given statistic which makes the known ...

A multivariate is a vector each of whose elements is a variate. The variates need not be independent, and if they are not, a correlation is said to exist between them. The ...

Given a random variable X with continuous and strictly monotonic probability density function f(X), a quantile function Q_f assigns to each probability p attained by f the ...