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An ordinal number alpha>0 is called a limit ordinal iff it has no immediate predecessor, i.e., if there is no ordinal number beta such that beta+1=alpha (Ciesielski 1997, p. ...

A number x such that for all epsilon>0, there exists a member of the set y different from x such that |y-x|<epsilon. The topological definition of limit point P of A is that ...

The Laplace transform is an integral transform perhaps second only to the Fourier transform in its utility in solving physical problems. The Laplace transform is particularly ...

An attracting set to which orbits or trajectories converge and upon which trajectories are periodic.

The scalar form of Laplace's equation is the partial differential equation del ^2psi=0, (1) where del ^2 is the Laplacian. Note that the operator del ^2 is commonly written ...

Laplace's integral is one of the following integral representations of the Legendre polynomial P_n(x), P_n(x) = 1/piint_0^pi(du)/((x+sqrt(x^2-1)cosu)^(n+1))du (1) = ...

The Laplace distribution, also called the double exponential distribution, is the distribution of differences between two independent variates with identical exponential ...

The spherical harmonics form a complete orthogonal system, so an arbitrary real function f(theta,phi) can be expanded in terms of complex spherical harmonics by ...

A one-sided (singly infinite) Laplace transform, L_t[f(t)](s)=int_0^inftyf(t)e^(-st)dt. This is the most common variety of Laplace transform and it what is usually meant by ...

A two-sided (doubly infinite) Laplace transform, L_t[f(t)](s)=int_(-infty)^inftyf(t)e^(-st)dt. While some authors use this as the primary definition of "the" Laplace ...