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The survival function describes the probability that a variate X takes on a value greater than a number x (Evans et al. 2000, p. 6). The survival function is therefore ...

The pathological function f_a(x)=sum_(k=1)^infty(sin(pik^ax))/(pik^a) (originally defined for a=2) that is continuous but differentiable only on a set of points of measure ...

Given a subset A of a larger set, the characteristic function chi_A, sometimes also called the indicator function, is the function defined to be identically one on A, and is ...

For a fractal process with values y(t-Deltat) and y(t+Deltat), the correlation between these two values is given by the Brown function r=2^(2H-1)-1, also known as the ...

A meromorphic function is a single-valued function that is analytic in all but possibly a discrete subset of its domain, and at those singularities it must go to infinity ...

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

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

A function with k continuous derivatives is called a C^k function. In order to specify a C^k function on a domain X, the notation C^k(X) is used. The most common C^k space is ...

The term "recursive function" is often used informally to describe any function that is defined with recursion. There are several formal counterparts to this informal ...

A function f(x_1,...,x_n) of one or more variables whose range is one-dimensional, as compared to a vector function, whose range is three-dimensional (or, in general, ...