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A moving average may generate an irregular oscillation even if none exists in the original data.

A moving average using 15 points having weights -3, -6, -5, 3, 21, 46, 67, 74, 67, 46, 21, 3, -5, -6, and -3. It is sometimes used by actuaries.

Strong convergence is the type of convergence usually associated with convergence of a sequence. More formally, a sequence {x_n} of vectors in a normed space (and, in ...

Variables x_i and x_j are said to be uncorrelated if their covariance is zero: cov(x_i,x_j)=0. Independent statistics are always uncorrelated, but the converse is not ...

Let the greatest term H of a sequence be a term which is greater than all but a finite number of the terms which are equal to H. Then H is called the upper limit of the ...

Let f_n(z) be a sequence of functions, each regular in a region D, let |f_n(z)|<=M for every n and z in D, and let f_n(z) tend to a limit as n->infty at a set of points ...

Weak convergence is usually either denoted x_nw; ->x or x_n->x. A sequence {x_n} of vectors in an inner product space E is called weakly convergent to a vector in E if ...

A generalized hypergeometric function _pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;z], is said to be k-balanced if sum_(i=1)^qbeta_i=k+sum_(i=1)^palpha_i.

sum_(y=0)^m(-1)^(m-y)q^((m-y; 2))[m; y]_q(1-wq^m)/(q-wq^y) ×(1-wq^y)^m(-(1-z)/(1-wq^y);q)_y=(1-z)^mq^((m; 2)), where [n; y]_q is a q-binomial coefficient.

The q-analog of the derivative, defined by (d/(dx))_qf(x)=(f(x)-f(qx))/(x-qx). (1) For example, (d/(dx))_qsinx = (sinx-sin(qx))/(x-qx) (2) (d/(dx))_qlnx = ...