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The triangle function is the function Lambda(x) = {0 |x|>=1; 1-|x| |x|<1 (1) = Pi(x)*Pi(x) (2) = Pi(x)*H(x+1/2)-Pi(x)*H(x-1/2), (3) where Pi(x) is the rectangle function, ...

A solution of a linear homogeneous ordinary differential equation with polynomial coefficients.

The rectangle function Pi(x) is a function that is 0 outside the interval [-1/2,1/2] and unity inside it. It is also called the gate function, pulse function, or window ...

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 ...

Generally speaking, a Green's function is an integral kernel that can be used to solve differential equations from a large number of families including simpler examples such ...

Consider the general system of two first-order ordinary differential equations x^. = f(x,y) (1) y^. = g(x,y). (2) Let x_0 and y_0 denote fixed points with x^.=y^.=0, so ...

A function defined for all possible input values.

A function f(x) is said to be nondecreasing on an interval I if f(b)>=f(a) for all b>a, where a,b in I. Conversely, a function f(x) is said to be nonincreasing on an interval ...

A partial function is a function that is not total.

The class of all regular sequences of particularly well-behaved functions equivalent to a given regular sequence. A distribution is sometimes also called a "generalized ...