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Let a distribution to be approximated be the distribution F_n of standardized sums Y_n=(sum_(i=1)^(n)(X_i-X^_))/(sqrt(sum_(i=1)^(n)sigma_X^2)). (1) In the Charlier series, ...

If F(x) is a probability distribution with zero mean and rho=int_(-infty)^infty|x|^3dF(x)<infty, (1) where the above integral is a stieltjes integral, then for all x and n, ...

The plane spanned by the three points x(t), x(t+h_1), and x(t+h_2) on a curve as h_1,h_2->0. Let z be a point on the osculating plane, then [(z-x),x^',x^('')]=0, where ...

A one-dimensional map whose increments are distributed according to a normal distribution. Let y(t-Deltat) and y(t+Deltat) be values, then their correlation is given by the ...

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 ...

The Hh-function is a function closely related to the normal distribution function. It can be defined using the auxilary functions Z(x) = 1/(sqrt(2pi))e^(-x^2/2) (1) Q(x) = ...

If x is a regular patch on a regular surface in R^3 with normal N^^, then x_(uu) = Gamma_(11)^1x_u+Gamma_(11)^2x_v+eN^^ (1) x_(uv) = Gamma_(12)^1x_u+Gamma_(12)^2x_v+fN^^ (2) ...

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all ...

Partial differential equation boundary conditions which give the normal derivative on a surface.

Let M be an oriented regular surface in R^3 with normal N. Then the support function of M is the function h:M->R defined by h(p)=p·N(p).