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An extended form of Bürmann's theorem. Let f(z) be a function of z analytic in a ring-shaped region A, bounded by another curve C and an inner curve c. Let theta(z) be a ...

The term "over" is commonly used in mathematical exposition as a synonym for "in the domain of." So, for example, "Let f be a function over the reals" means "Let f be a ...

The operator partial^_ is defined on a complex manifold, and is called the 'del bar operator.' The exterior derivative d takes a function and yields a one-form. It decomposes ...

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 ...

The computation of points or values between ones that are known or tabulated using the surrounding points or values. In particular, given a univariate function f=f(x), ...

Partial evaluation is a branch of computer science studying program transformation via specialization. Any function can be specialized by fixing one or more of its inputs to ...

In the fields of functional and harmonic analysis, the Littlewood-Paley decomposition is a particular way of decomposing the phase plane which takes a single function and ...

where _3F_2(a,b,c;d,e;z) is a generalized hypergeometric function and Gamma(z) is the gamma function (Bailey 1935, p. 16; Koepf 1998, p. 32).

The function K_n(x_0,x)=K_n(x,x_0)^_=K_n(x^_,x^__0) which is useful in the study of many polynomials.

A function used to study ordinary differential equations.