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Informally, an L^2-function is a function f:X->R that is square integrable, i.e., |f|^2=int_X|f|^2dmu with respect to the measure mu, exists (and is finite), in which case ...

A formal logic developed by Alonzo Church and Stephen Kleene to address the computable number problem. In the lambda calculus, lambda is defined as the abstraction operator. ...

The ordinary differential equation (1) (Byerly 1959, p. 255). The solution is denoted E_m^p(x) and is known as an ellipsoidal harmonic of the first kind, or Lamé function. ...

An integral transform which is often written as an ordinary Laplace transform involving the delta function. The Laplace transform and Dirichlet series are special cases of ...

In bispherical coordinates, Laplace's equation becomes (1) Attempt separation of variables by plugging in the trial solution f(u,v,phi)=sqrt(coshv-cosu)U(u)V(v)Psi(psi), (2) ...

A law is a mathematical statement which always holds true. Whereas "laws" in physics are generally experimental observations backed up by theoretical underpinning, laws in ...

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

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 ...

A bounded entire function in the complex plane C is constant. The fundamental theorem of algebra follows as a simple corollary.

lnx is the notation used in physics and engineering to denote the logarithm to base e, also called the natural logarithm, i.e., lnx=log_ex. The United States Department of ...