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A derivative of a complex function, which must satisfy the Cauchy-Riemann equations in order to be complex differentiable.

A G-space is a special type of T1-Space. Consider a point x and a homeomorphism of an open neighborhood V of x onto an open set of R^n. Then a space is a G-space if, for any ...

A Lie groupoid over B is a groupoid G for which G and B are differentiable manifolds and alpha,beta and multiplication are differentiable maps. Furthermore, the derivatives ...

A function with k continuous derivatives is called a C^k function. In order to specify a C^k function on a domain X, the notation C^k(X) is used. The most common C^k space is ...

If g(x) is differentiable at the point x and f(x) is differentiable at the point g(x), then f degreesg is differentiable at x. Furthermore, let y=f(g(x)) and u=g(x), then ...

A synonym for analytic function, regular function, differentiable function, complex differentiable function, and holomorphic map (Krantz 1999, p. 16). The word derives from ...

The pathological function f_a(x)=sum_(k=1)^infty(sin(pik^ax))/(pik^a) (originally defined for a=2) that is continuous but differentiable only on a set of points of measure ...

The Blancmange function, also called the Takagi fractal curve (Peitgen and Saupe 1988), is a pathological continuous function which is nowhere differentiable. Its name ...

There are several commonly used methods of defining the slippery, but extremely important, concept of a continuous function (which, depending on context, may also be called a ...

If M is continuous and int_a^bM(x)h(x)dx=0 for all infinitely differentiable h(x), then M(x)=0 on the open interval (a,b).