Holomorphic Functions

By | 2015-11-15

In mathematics, holomorphic functions are the central objects of study in complex analysis. A holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain. The existence of a complex derivative in a neighborhood is a very strong condition, for it implies that any holomorphic function is actually infinitely differentiable and equal to its own Taylor series.

 

Holomorphic functions are also sometimes referred to as regular functions[2] or as conformal maps. A holomorphic function whose domain is the whole complex plane is called an entire function. The phrase “holomorphic at a point z0” means not just differentiable at z0, but differentiable everywhere within some neighborhood of z0 in the complex plane.

 

The foundation of all location-based apps and services is the ability to determine where the user is located. Then, for applications such as navigation and augmented reality, direction of travel or the direction the user is facing are vital pieces of information as well.

 

 

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