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...
8 KB (1,114 words) - 23:59, 30 August 2024
\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...
90 KB (13,365 words) - 22:20, 23 August 2024
Zeros and poles (redirect from Pole (of a function))
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...
9 KB (1,479 words) - 15:16, 16 June 2024
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...
6 KB (1,117 words) - 13:15, 3 July 2024
contrast to the term meromorphic derived from μέρος (méros) meaning "part". A holomorphic function resembles an entire function ("whole") in a domain...
24 KB (3,334 words) - 02:45, 20 August 2024
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...
18 KB (3,277 words) - 09:01, 3 September 2024
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...
124 KB (17,658 words) - 20:14, 19 August 2024
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...
25 KB (4,386 words) - 22:51, 27 August 2024
{\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...
68 KB (10,314 words) - 06:07, 4 September 2024
In mathematics, an L-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. An L-series...
8 KB (984 words) - 11:59, 7 May 2024