\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 (13,397 words) - 05:21, 21 April 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 (1,477 words) - 04:06, 6 April 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 (3,249 words) - 00:26, 11 March 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 (1,035 words) - 01:12, 24 December 2023 |
contrast to the term meromorphic derived from μέρος (méros) meaning "part". A holomorphic function resembles an entire function ("whole") in a domain... 23 KB (2,820 words) - 06:03, 13 April 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... 123 KB (17,583 words) - 02:52, 15 March 2024 |
Analytic continuation (redirect from Meromorphic continuation) (s)\right)\end{aligned}}} Finally, since the gamma function has a meromorphic continuation to C ∖ N {\displaystyle \mathbb {C} \setminus \mathbb... 33 KB (6,793 words) - 15:49, 26 February 2024 |
Modular form (redirect from Modular function) Instead, modular functions are meromorphic: they are holomorphic on the complement of a set of isolated points, which are poles of the function. A modular form... 31 KB (4,611 words) - 03:00, 12 April 2024 |
a transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function. In other words, a... 13 KB (1,662 words) - 13:00, 16 January 2024 |
derivative exists in this more general region, making the zeta function a meromorphic function. The above equation no longer applies for these extended values... 24 KB (3,253 words) - 13:38, 5 March 2024 |
and poles of a meromorphic function to a contour integral of the function's logarithmic derivative. If f(z) is a meromorphic function inside and on some... 9 KB (1,540 words) - 01:37, 4 January 2024 |
questions in several complex variables, concerning the existence of meromorphic functions that are specified in terms of local data. They were introduced... 8 KB (1,170 words) - 17:42, 11 January 2024 |
meromorphic functions. The function field of a variety is then the set of all meromorphic functions on the variety. (Like all meromorphic functions,... 5 KB (683 words) - 13:29, 31 March 2024 |
Rational functions are representative examples of meromorphic functions. Iteration of rational functions (maps) on the Riemann sphere creates discrete dynamical... 16 KB (2,355 words) - 13:42, 3 April 2024 |
Residue (complex analysis) (redirect from Residue of an analytic function) integral of a meromorphic function along a path enclosing one of its singularities. (More generally, residues can be calculated for any function f : C ∖ {... 15 KB (3,079 words) - 20:02, 20 April 2024 |
elliptic functions are special kinds of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because they... 16 KB (2,444 words) - 16:15, 24 April 2024 |
distributions. The Laplace transform of the Heaviside step function is a meromorphic function. Using the unilateral Laplace transform we have: H ^ ( s )... 14 KB (1,988 words) - 12:59, 30 March 2024 |
Riemann sphere (section Rational functions) function mapping to infinity. More generally, any meromorphic function can be thought of as a holomorphic function whose codomain is the Riemann sphere. In geometry... 21 KB (3,325 words) - 01:46, 13 April 2024 |
Nevanlinna theory (category Meromorphic functions) of complex analysis, Nevanlinna theory is part of the theory of meromorphic functions. It was devised in 1925, by Rolf Nevanlinna. Hermann Weyl called... 17 KB (2,603 words) - 12:55, 4 May 2023 |
mathematics, an algebraic function is a function that can be defined as the root of an irreducible polynomial equation. Algebraic functions are often algebraic... 12 KB (1,944 words) - 10:25, 28 February 2024 |
associated entire function with zeroes at precisely the points of that sequence. A generalization of the theorem extends it to meromorphic functions and allows... 10 KB (1,872 words) - 12:17, 9 April 2024 |
the Hasse–Weil zeta function attached to an algebraic variety V defined over an algebraic number field K is a meromorphic function on the complex plane... 9 KB (1,304 words) - 16:29, 20 March 2024 |
Normal family (category Topology of function spaces) function from X to Y is called a meromorphic function, and so each limit point of a normal family of meromorphic functions is a meromorphic function.... 8 KB (1,060 words) - 15:46, 26 January 2024 |