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The finite difference is the discrete analog of the derivative. The finite forward difference of a function f_p is defined as Deltaf_p=f_(p+1)-f_p, (1) and the finite ...

The logarithmic integral (in the "American" convention; Abramowitz and Stegun 1972; Edwards 2001, p. 26), is defined for real x as li(x) = {int_0^x(dt)/(lnt) for 0<x<1; ...

The natural logarithm lnx is the logarithm having base e, where e=2.718281828.... (1) This function can be defined lnx=int_1^x(dt)/t (2) for x>0. This definition means that e ...

Gamma functions of argument 2z can be expressed in terms of gamma functions of smaller arguments. From the definition of the beta function, ...

An operator relating the past asymptotic state of a dynamical system governed by the Schrödinger equation id/(dt)psi(t)=Hpsi(t) to its future asymptotic state.

For a linear homogeneous ordinary differential equation, if y_1(x) and y_2(x) are solutions, then so is y_1(x)+y_2(x).

The partial differential equation u_(xy)+alphau_x+betau_y+gammau_xu_y=0.

Written in the notation of partial derivatives, the d'Alembertian square ^2 in a flat spacetime is defined by square ^2=del ^2-1/(c^2)(partial^2)/(partialt^2), where c is the ...

The incenter I is the center of the incircle for a polygon or insphere for a polyhedron (when they exist). The corresponding radius of the incircle or insphere is known as ...

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!! ...