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Riemann's moduli space R_p is the space of analytic equivalence classes of Riemann surfaces of fixed genus p.

X subset= R^n is semianalytic if, for all x in R^n, there is an open neighborhood U of x such that X intersection U is a finite Boolean combination of sets {x^_ in ...

The integral int_0^thetae^(-xsecphi)dphi.

The single bar | is a notation variously used to denote the absolute value |x|, complex modulus |z|, vector norm |x|, determinant |A|, or "divides" (a|b).

The function from a given nonempty set X to the power set P(X) that maps every element x of X to the set {x}.

A function possessing a single period in the complex plane is said to be singly periodic, of often simply periodic. Singly periodic functions include the trigonometric ...

A function f(x) is said to be strictly decreasing on an interval I if f(b)<f(a) for all b>a, where a,b in I. On the other hand, if f(b)<=f(a) for all b>a, the function is ...

A function f(x) is said to be strictly increasing on an interval I if f(b)>f(a) for all b>a, where a,b in I. On the other hand, if f(b)>=f(a) for all b>a, the function is ...

The topological completion C of a field F with respect to the absolute value |·| is the smallest field containing F for which all Cauchy sequences or rationals converge.

A function which is not an algebraic function. In other words, a function which "transcends," i.e., cannot be expressed in terms of, algebra. Examples of transcendental ...