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A monotonic function is a function which is either entirely nonincreasing or nondecreasing. A function is monotonic if its first derivative (which need not be continuous) ...

In the archaic terminology of Whittaker and Watson (1990), the complex number z representing x+iy.

A Banach limit is a bounded linear functional f on the space ł^infty of complex bounded sequences that satisfies ||f||=f(1)=1 and f({a_(n+1)})=f({a_n}) for all {a_n} in ...

Let mu be a positive measure on a sigma-algebra M, and let lambda be an arbitrary (real or complex) measure on M. If there is a set A in M such that lambda(E)=lambda(A ...

Legendre and Whittaker and Watson's (1990) term for the beta integral int_0^1x^p(1-x)^qdx, whose solution is the beta function B(p+1,q+1).

An extreme point of a subset K of a vector space X is an extreme set S of K which consists of a single point x in K. The collection of all extreme points of K is sometimes ...

A function of more than one variable.

A subset E of a topological space S is said to be nonmeager if E is of second category in S, i.e., if E cannot be written as the countable union of subsets which are nowhere ...

The norm topology on a normed space X=(X,||·||_X) is the topology tau consisting of all sets which can be written as a (possibly empty) union of sets of the form B_r(x)={y in ...

Let H be a Hilbert space, B(H) the set of bounded linear operators from H to itself, T an operator on H, and sigma(T) the operator spectrum of T. Then if T in B(H) and T is ...