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Given a Poisson distribution with rate of change lambda, the distribution of waiting times between successive changes (with k=0) is D(x) = P(X<=x) (1) = 1-P(X>x) (2) = ...

In the most commonly used convention (e.g., Apostol 1967, pp. 202-204), the first fundamental theorem of calculus, also termed "the fundamental theorem, part I" (e.g., Sisson ...

The first Napoleon point N, also called the outer Napoleon point, is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of ...

The intersection Fl of the Gergonne line and the Soddy line. In the above figure, D^', E^', and F^' are the Nobbs points, I is the incenter, Ge is the Gergonne point, and S ...

A formal power series, sometimes simply called a "formal series" (Wilf 1994), of a field F is an infinite sequence {a_0,a_1,a_2,...} over F. Equivalently, it is a function ...

Given a semicircular hump f(x) = sqrt(L^2-(x-L)^2) (1) = sqrt((2L-x)x), (2) the Fourier coefficients are a_0 = 1/2piL (3) a_n = ((-1)^nLJ_1(npi))/n (4) b_n = 0, (5) where ...

F_x[cos(2pik_0x)](k) = int_(-infty)^inftye^(-2piikx)((e^(2piik_0x)+e^(-2piik_0x))/2)dx (1) = 1/2int_(-infty)^infty[e^(-2pii(k-k_0)x)+e^(-2pii(k+k_0)x)]dx (2) = ...

F_x[sin(2pik_0x)](k) = int_(-infty)^inftye^(-2piikx)((e^(2piik_0x)-e^(-2piik_0x))/(2i))dx (1) = 1/2iint_(-infty)^infty[-e^(-2pii(k-k_0)x)+e^(-2pii(k+k_0)x)]dx (2) = ...

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 ...

The study of an extension of derivatives and integrals to noninteger orders. Fractional calculus is based on the definition of the fractional integral as ...