Search results
Jump to navigation
Jump to search
Page title matches
- ...nction'' see [[Iterated function]]. For compositions of a finite number of functions, useful in [[fractal]] theory, see [[Iterated function system]]. ...analytic functions, there are results for more general [[Complex analysis|functions of a complex variable]] as well. ...26 KB (4,221 words) - 09:10, 20 January 2025
Page text matches
- {{Short description|Solution of equation with analytic coefficients}} are [[analytic function]]s. So ''y''(''z'') is an algebroid function if it satisfies ...1 KB (150 words) - 09:52, 28 November 2024
- ...' are sequences of polynomials <math>\Phi_n^{(r)}(z)</math> defined from [[analytic function]]s <math>B</math> and <math>C</math> by [[generating function]]s o ...last2=Buck | first2=R. Creighton | title=Polynomial expansions of analytic functions | url=https://books.google.com/books?id=eihMuwkh4DsC | publisher=[[Springer ...1,000 bytes (138 words) - 06:57, 13 May 2024
- ...ons]]. It is another name for the stronger version of [[Montel%27s theorem#Functions omitting two values|Montel's theorem]]. Let <math>\mathcal{F} </math> be a family of analytic functions defined on a domain <math> \Omega </math>. If there are two fixed complex n ...1,003 bytes (147 words) - 15:51, 1 August 2022
- {{Short description|Generalization of analytic functions}} ...=1951|year3=1953|year4=1956}} that generalize [[Analytic function|analytic functions]] and satisfy a weakened form of the [[Cauchy–Riemann equations]]. ...4 KB (530 words) - 20:18, 17 June 2023
- ...[neighbourhood (mathematics)|neighbourhood]] of <math>x_0</math> (since an analytic function must equals the sum of its [[Taylor series]]). is flat at <math>x = 0</math>. Thus, this is an example of a [[non-analytic smooth function]]. The pathological nature of this example is partially ill ...2 KB (307 words) - 16:20, 26 January 2024
- ...e of [[zeta function]] introduced by [[Kohji Matsumoto]] in 1990. They are functions of the form ...mr=1071754 | year=1990 | volume=1434 | chapter=Value-distribution of zeta-functions| pages=178–187 | isbn=978-3-540-52787-9 }} ...708 bytes (91 words) - 23:37, 25 January 2023
- ...[[Bieberbach conjecture]]. Finding similar estimates for other classes of functions is called the '''Fekete–Szegő problem'''. is a univalent analytic function on the unit disk and <math>0\leq \lambda < 1</math>, then ...1 KB (151 words) - 03:44, 17 April 2024
- ...field of real numbers by restricted pfaffian functions and the exponential functions'', J. Amer. Math. Soc. '''9''' (1996), pp. 1051–1094.</ref> In terms of [[Analytic geometry#Modern analytic geometry|analytic geometry]], the theorem states that any [[definable set]] in the above lang ...5 KB (712 words) - 18:55, 16 July 2021
- ...ero on all of [''a'',''b'']. Quasi-analytic classes are broader classes of functions for which this statement still holds true. ...be a sequence of positive real numbers. Then the Denjoy-Carleman class of functions ''C''<sup>''M''</sup>([''a'',''b'']) is defined to be those ''f'' &isi ...8 KB (1,329 words) - 10:05, 7 November 2023
- ...]] from real functions to complex functions, taking the role that for real functions is played by the number of zeros of the function in an [[interval (mathemat ...I(f)</math> of a complex-valued function ''f'' that is [[analytic function|analytic]] in a complex [[Neighbourhood (mathematics)|neighbourhood]] of the real in ...2 KB (334 words) - 09:15, 21 January 2025
- {{about|Siegel G-functions|the general functions introduced by Cornelius Meijer|Meijer G-function}} In [[mathematics]], the '''Siegel G-functions''' are a class of functions in [[transcendental number theory]] introduced by [[C. L. Siegel]]. They s ...2 KB (318 words) - 12:25, 19 February 2025
- ...ains can also be generalized <ref name='ency_math'/> in a manner such that functions which are monogenic over non-connected subsets of <math> \mathbb{C} </math> [[Category:Functions and mappings]] ...2 KB (296 words) - 22:31, 9 August 2024
- ...lize the [[Schwarz reflection principle]] to reflection across arbitrary [[analytic curve]]s, not just across the real axis. ...pen neighborhood]] <math>\Omega</math> of <math>\Gamma</math> and a unique analytic function <math>S</math> on <math>\Omega</math> such that <math>S(z) = \over ...4 KB (579 words) - 09:42, 28 November 2024
- ...ort description|Theorem in complex analysis about the sheaf of holomorphic functions}} ...h> (and subsequently the sheaf <math>\mathcal{O}_{X}</math> of holomorphic functions on a [[complex manifold]] <math>X</math>) is [[coherent sheaf|coherent]].<r ...2 KB (297 words) - 21:44, 26 October 2024
- | title = Analytic Functions of Several Complex Variables ...s an invertible matrix for each ''z'' in ''K''. Then there exist analytic functions <math>F'</math> in <math>K'</math> and <math>F''</math> in <math>K''</math ...3 KB (406 words) - 17:31, 10 May 2021
- ...ofunctions. Semantically, it is the application of algebraic operations on analytic quantities. As a research programme, it was started by the Japanese mathema ...] ''n'', and let ''X'' be its complexification. The sheaf of '''microlocal functions''' on ''M'' is given as{{sfn|Kashiwara|Schapira|1990|loc=Definition 11.5.1} ...4 KB (485 words) - 09:52, 16 August 2023
- {{short description|Subset of complex n-space bounded by analytic functions}} ...[[Function of several complex variables|several complex variables]], an '''analytic polyhedron''' is a subset of the [[Complex coordinate space|complex space]] ...5 KB (632 words) - 22:59, 9 September 2023
- ...istence theorem|existence]] and uniqueness theorem for [[analytic function|analytic]] [[partial differential equation]]s associated with [[Cauchy problem|Cauch ...e [[analytic function]]s. The theorem and its proof are valid for analytic functions of either real or complex variables. ...7 KB (1,076 words) - 21:27, 10 November 2023
- ...>\log^+(x)=\max[0,\log(x)]</math>. Being the ratio of two bounded analytic functions is a sufficient condition for a function to be of bounded type (defined in Functions of bounded type are not necessarily bounded, nor do they have a property ca ...8 KB (1,470 words) - 21:08, 11 August 2024
- ...ifford|last2=Rossi|first2=Hugo|year=2009|url={{Google books|title=Analytic Functions of Several Complex Variables|wsqFAwAAQBAJ|page=2|plainurl=yes}}}} ...2 KB (280 words) - 06:56, 26 February 2025