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Let s(n)=sigma(n)-n, where sigma(n) is the divisor function and s(n) is the restricted divisor function, and define the aliquot sequence of n by ...

Bessel's correction is the factor (N-1)/N in the relationship between the variance sigma and the expectation values of the sample variance, <s^2>=(N-1)/Nsigma^2, (1) where ...

A theorem proved by Doob (1942) which states that any random process which is both normal and Markov has the following forms for its correlation function C_y(tau), spectral ...

A curve on the unit sphere S^2 is an eversion if it has no corners or cusps (but it may be self-intersecting). These properties are guaranteed by requiring that the curve's ...

Given a sequence of independent random variates X_1, X_2, ..., if sigma_k^2=var(X_k) and rho_n^2=max_(k<=n)((sigma_k^2)/(s_n^2)), then lim_(n->infty)rho_n^2=0. This means ...

The ratio X/Y of independent normally distributed variates with zero mean is distributed with a Cauchy distribution. This can be seen as follows. Let X and Y both have mean 0 ...

Given a statistical distribution with measured mean, mode, and standard deviation sigma, the Pearson mode skewness is (mean-mode)/sigma. The function was incorrectly ...

Regular expressions define formal languages as sets of strings over a finite alphabet. Let sigma denote a selected alphabet. Then emptyset is a regular expression that ...

The Sharpe ratio is a risk-adjusted financial measure developed by Nobel Laureate William Sharpe. It uses a fund's standard deviation and excess return to determine the ...

Given the left factorial function Sigma(n)=sum_(k=1)^nk!, SK(p) for p prime is the smallest integer n such that p|1+Sigma(n-1). The first few known values of SK(p) are 2, 4, ...