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A pair of functions phi_i(x) and phi_j(x) are orthonormal if they are orthogonal and each normalized so that int_a^b[phi_i(x)]^2w(x)dx = 1 (1) int_a^b[phi_j(x)]^2w(x)dx = 1. ...

The variation of a function which exhibits slope changes, also called the saltus of a function. A series may also oscillate, causing it not to converge.

Let gamma be a path given parametrically by sigma(t). Let s denote arc length from the initial point. Then int_gammaf(s)ds = int_a^bf(sigma(t))|sigma^'(t)|dt (1) = ...

The kth percentile P_k is that value of x, say x_k, which corresponds to a cumulative frequency of Nk/100, where N is the sample size.

The interval (generally, the smallest interval) over which the values of a periodic function recur. Functions may have one or more periods over time and in space.

An upper semicontinuous function whose restrictions to all complex lines are subharmonic (where defined). These functions were introduced by P. Lelong and Oka in the early ...

Let f:R->R, then the positive part of f is the function f^+:R->R defined by f^+(x)=max(f(x),0) The positive part satisfies the identity f=f^+-f^-, where f^- is the negative ...

The positive real axis is the portion of the real axis with x>0.

Let C^omega(I) be the set of real analytic functions on I. Then C^omega(I) is a subalgebra of C^infty(I). A necessary and sufficient condition for a function f in C^infty(I) ...

A complex number z is said to be purely imaginary if it has no real part, i.e., R[z]=0. The term is often used in preference to the simpler "imaginary" in situations where z ...