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Let |sum_(n=1)^pa_n|<K, (1) where K is independent of p. Then if f_n>=f_(n+1)>0 and lim_(n->infty)f_n=0, (2) it follows that sum_(n=1)^inftya_nf_n (3) converges.

A version of fractal dimension used in time-series analysis.

There are two sets of constants that are commonly known as Lebesgue constants. The first is related to approximation of function via Fourier series, which the other arises in ...

Predictability at a time tau in the future is defined by (R(x(t),x(t+tau)))/(H(x(t))), and linear predictability by (L(x(t),x(t+tau)))/(H(x(t))), where R and L are the ...

The study of sampling

Stirling's approximation gives an approximate value for the factorial function n! or the gamma function Gamma(n) for n>>1. The approximation can most simply be derived for n ...

psi=(A_0+alpha_1A_1+alpha_2A_2+...)e^(iS/alpha).

There are several closely related results that are variously known as the binomial theorem depending on the source. Even more confusingly a number of these (and other) ...

The natural logarithm of 2 is a transcendental quantity that arises often in decay problems, especially when half-lives are being converted to decay constants. ln2 has ...

An algorithm which extrapolates the partial sums s_n of a series sum_(n)a_n whose convergence is approximately geometric and accelerates its rate of convergence. The ...