mathematical field of complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except...

\Re (z)>0\,.} The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in...

poles, that is fundamental for the study of meromorphic functions. For example, if a function is meromorphic on the whole complex plane plus the point at...

contrast to the term meromorphic derived from μέρος (méros) meaning "part". A holomorphic function resembles an entire function ("whole") in a domain...

concerns the existence of meromorphic functions with prescribed poles. Conversely, it can be used to express any meromorphic function as a sum of partial fractions...

role in the theory of elliptic functions, i.e., meromorphic functions that are doubly periodic. A ℘-function together with its derivative can be used to parameterize...

field. Patching the local data of meromorphic functions, i.e. the problem of creating a global meromorphic function from zeros and poles, is called the...

{\displaystyle \lim _{s\to 1}(s-1)\zeta (s)=1.} Thus the Riemann zeta function is a meromorphic function on the whole complex plane, which is holomorphic everywhere...

analytically to an entire function. A transcendental entire function is an entire function that is not a polynomial. Just as meromorphic functions can be viewed as...

definition of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example in a new region where...