Search Results for ""

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

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

There are several commonly used methods of defining the slippery, but extremely important, concept of a continuous function (which, depending on context, may also be called a ...

The inverse of the Laplace transform F(t) = L^(-1)[f(s)] (1) = 1/(2pii)int_(gamma-iinfty)^(gamma+iinfty)e^(st)f(s)ds (2) f(s) = L[F(t)] (3) = int_0^inftyF(t)e^(-st)dt. (4)

The study, first developed by Boole, of shift-invariant operators which are polynomials in the differential operator D^~. Heaviside calculus can be used to solve any ordinary ...

In bipolar coordinates, the Helmholtz differential equation is not separable, but Laplace's equation is.

P_n(cosalpha)=(sqrt(2))/piint_0^alpha(cos[(n+1/2)phi])/(sqrt(cosphi-cosalpha))dphi, where P_n(x) is a Legendre polynomial.

A shortened term for integral transform. Geometrically, if S and T are two transformations, then the similarity transformation TST^(-1) is sometimes called the transform ...

Differential Equations

If F(x) is a probability distribution with zero mean and rho=int_(-infty)^infty|x|^3dF(x)<infty, (1) where the above integral is a stieltjes integral, then for all x and n, ...