When a particle moves, the Cartesian system is inadequate to describe its path. Instead, the particle's location must become a function of time. This function is described with a pair of equations for a location. With "t" representing time in most applications, the particle's location is described as x=f(t) and y=g(t).
Meromorphic functions allow the projection of the path of the curve. The restrictions of the two-coordinate system can be adjusted by adding a third coordinate sometimes designated "z." The projected path is done on a complex plane designated by "C." Both "P1" and "P2" comprise the points on the complex plane, with "D" is a subdomain of P1. Letters "f" and "g" are non-constant and a function of the complex variable.
Meromorphic functions have allowed the formulation of a number of theorems addressing factorization and sharing value problems. There is the belief that these functions can be used in a number of mathematics, thanks to the transcendental functions of the factors.