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The z-score associated with the ith observation of a random variable x is given by z_i=(x_i-x^_)/sigma, where x^_ is the mean and sigma the standard deviation of all ...

The vector triple product identity Ax(BxC)=B(A·C)-C(A·B). This identity can be generalized to n dimensions,

A Bäcklund transformation allows additional solutions to a nonlinear partial differential equations to be found if one particular solution is already known.

In order to find a root of a polynomial equation a_0x^n+a_1x^(n-1)+...+a_n=0, (1) consider the difference equation a_0y(t+n)+a_1y(t+n-1)+...+a_ny(t)=0, (2) which is known to ...

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 ...

An interpolation formula, sometimes known as the Newton-Bessel formula, given by (1) for p in [0,1], where delta is the central difference and B_(2n) = 1/2G_(2n) (2) = ...

The differential equation obtained by applying the biharmonic operator and setting to zero: del ^4phi=0. (1) In Cartesian coordinates, the biharmonic equation is del ^4phi = ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_5=f(x_5). Then Boole's rule approximating the ...

Catalan's constant is a constant that commonly appears in estimates of combinatorial functions and in certain classes of sums and definite integrals. It is usually denoted K ...

For any system that seeks to minimize a function, only seven different local forms of catastrophe "typically" occur for four or fewer variables: 1. Fold catastrophe, 2. Cusp ...