Intuitively, a meromorphic function is a ratio of two well-behaved (holomorphic) functions. Such a function will still be well-behaved, except possibly at the points where the denominator of the fraction …

Dec 3, 2025 · A meromorphic function is a single-valued function that is analytic in all but possibly a discrete subset of its domain, and at those singularities it must go to infinity like a polynomial (i.e., …

A function that is analytic on a region A is called holomorphic on A. A function that is analytic on A except for a set of poles of finite order is called meromorphic on A.

ition 0.1. The class of meromorphic function forms a . ld over C. That is, given any meromorphic functions f; g; h 2 M( ), w. 1=f 2 M. Recall that if a holomorphic function has nitely many roots, then it …

Corollary 4.2.2 Every meromorphic function f : C → C∞ is the quotient a/b of two entire functions a and b.

A meromorphic function is the ratio of two analytic functions which are analytic except for isolated singularities, called “ poles.” The word meromorphic comes from the Greek words meros (“part”) and …

Nov 2, 2025 · The set of all meromorphic functions on a subdomain of the complex plane has an advantage over the set of holomorphic functions: it forms not only a ring but also a field.

A meromorphic function in the complex plane that is either holomorphic at infinity or has a pole at infinity is said to be meromorphic in the extended complex plane.

PHIC FUNCTIONS A function f : ! C on an open set C is called meromorphic if it is homomorp. ic on except at a set of poles. In particular, holomo. phic functions are meromorphic. We note that a …

The sheaves of meromorphic sections aren't quasi-coherent modules in general, but they do have some properties in common with quasi-coherent modules.