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Let any finite or infinite set of points having no finite limit point be prescribed, and associate with each of its points a definite positive integer as its order. Then ...

Any real function u(x,y) with continuous second partial derivatives which satisfies Laplace's equation, del ^2u(x,y)=0, (1) is called a harmonic function. Harmonic functions ...

A function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. The space of locally integrable ...

The Riemann theta function is a complex function of g complex variables that occurs in the construction of quasi-periodic solutions of various equations in mathematical ...

A doubly periodic function with periods 2omega_1 and 2omega_2 such that f(z+2omega_1)=f(z+2omega_2)=f(z), (1) which is analytic and has no singularities except for poles in ...

The space of continuously differentiable functions is denoted C^1, and corresponds to the k=1 case of a C-k function.

The property intf(y)delta(x-y)dy=f(x) obeyed by the delta function delta(x).

A function f(x) is said to be square integrable if int_(-infty)^infty|f(x)|^2dx is finite.

The function defined by y_+^alpha={y^alpha for y>0; 0 for y<=0. (1)

k_nu(x)=(e^(-x))/(Gamma(1+1/2nu))U(-1/2nu,0,2x) for x>0, where U is a confluent hypergeometric function of the second kind.