Meromorfia

Meromorfia is a concept in complex analysis that describes functions which are analytic everywhere on a given domain except for a discrete set of isolated points where they exhibit poles. A function is said to be meromorphic on a domain if it is analytic on that domain, with the possible exception of a collection of isolated points at which the function has poles. This means that in the neighborhood of each such point, the function can be expressed as a ratio of two analytic functions, where the denominator is zero at that point and the numerator is non-zero. Alternatively, a meromorphic function can be viewed as a ratio of two entire functions, where the denominator is not identically zero. The set of poles of a meromorphic function is always a discrete set, meaning that each pole is isolated and there are no limit points within the domain. This property is crucial as it distinguishes meromorphic functions from functions with essential singularities. Meromorphic functions are fundamental in complex analysis and play a significant role in various areas of mathematics and physics, including the study of differential equations and algebraic geometry. They possess many well-behaved properties, such as forming a field under addition, subtraction, multiplication, and division.