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If A and B are equal by definition (i.e., A is defined as B), then this is written symbolically as A=B, A:=B, or sometimes A≜B.

The Lyapunov characteristic exponent [LCE] gives the rate of exponential divergence from perturbed initial conditions. To examine the behavior of an orbit around a point ...

The term "over" is commonly used in mathematical exposition as a synonym for "in the domain of." So, for example, "Let f be a function over the reals" means "Let f be a ...

The nth central binomial coefficient is defined as (2n; n) = ((2n)!)/((n!)^2) (1) = (2^n(2n-1)!!)/(n!), (2) where (n; k) is a binomial coefficient, n! is a factorial, and n!! ...

In his last letter to Hardy, Ramanujan defined 17 Jacobi theta function-like functions F(q) with |q|<1 which he called "mock theta functions" (Watson 1936ab, Ramanujan 1988, ...

A normal distribution in a variate X with mean mu and variance sigma^2 is a statistic distribution with probability density function ...

The G-transform of a function f(x) is defined by the integral (Gf)(x)=(G_(pq)^(mn)|(a_p); (b_q)|f(t))(x) (1) =1/(2pii)int_sigmaGamma[(b_m)+s, 1-(a_n)-s; (a_p^(n+1))+s, ...

If there are two functions F_1(t) and F_2(t) with the same integral transform T[F_1(t)]=T[F_2(t)]=f(s), (1) then a null function can be defined by delta_0(t)=F_1(t)-F_2(t) ...

The Hilbert transform (and its inverse) are the integral transform g(y) = H[f(x)]=1/piPVint_(-infty)^infty(f(x)dx)/(x-y) (1) f(x) = ...

Given a Poisson distribution with a rate of change lambda, the distribution function D(x) giving the waiting times until the hth Poisson event is D(x) = ...