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The nesting of two or more functions to form a single new function is known as composition. The composition of two functions f and g is denoted f degreesg, where f is a ...

Analytic continuation gives an equivalence relation between function elements, and the equivalence classes induced by this relation are called global analytic functions.

A graph or directed graph together with a function which assigns a positive real number to each edge (Harary 1994, p. 52).

The number of different triangles which have integer side lengths and perimeter n is T(n) = P(n,3)-sum_(1<=j<=|_n/2_|)P(j,2) (1) = [(n^2)/(12)]-|_n/4_||_(n+2)/4_| (2) = ...

A Maclaurin series is a Taylor series expansion of a function about 0, (1) Maclaurin series are named after the Scottish mathematician Colin Maclaurin. The Maclaurin series ...

Thomae's theorem, also called Thomae's transformation, is the generalized hypergeometric function identity (1) where Gamma(z) is the gamma function, _3F_2(a,b,c;e,f;z) is a ...

Let q be a positive integer, then Gamma_0(q) is defined as the set of all matrices [a b; c d] in the modular group Gamma Gamma with c=0 (mod q). Gamma_0(q) is a subgroup of ...

The set lambda of linear Möbius transformations w which satisfy w(t)=(at+b)/(ct+d), where a and d are odd and b and c are even. lambda is a subgroup of the modular group ...

A^*(x)=sum_(lambda_n<=x)^'a_n=1/(2pii)int_(c-iinfty)^(c+iinfty)f(s)(e^(sx))/sds, where f(s)=suma_ne^(-lambda_ns).

A set function mu possesses countable additivity if, given any countable disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...