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Also known as the alternating series test. Given a series sum_(n=1)^infty(-1)^(n+1)a_n with a_n>0, if a_n is monotonic decreasing as n->infty and lim_(n->infty)a_n=0, then ...

An attracting set to which orbits or trajectories converge and upon which trajectories are periodic.

An operator L^~ is said to be linear if, for every pair of functions f and g and scalar t, L^~(f+g)=L^~f+L^~g and L^~(tf)=tL^~f.

A function f which may (but does not necessarily) associate a given member of the range of f with more than one member of the domain of f. For example, trigonometric ...

The sequence generated by repeated application of a map. The map is said to have a closed orbit if it has a finite number of elements.

A set considered together with the sigma-algebra on the set.

A minimization of the maximum error for a fixed number of terms.

A function periodic with period 2pi such that p(theta+pi)=-p(theta) for all theta is said to be Möbius periodic.

Always increasing; never remaining constant or decreasing. Also called strictly increasing.

A sequence {a_n} such that either (1) a_(i+1)>=a_i for every i>=1, or (2) a_(i+1)<=a_i for every i>=1.