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- [[File:KellerDoyaT.png|300px|thumb|Transfer functions of laser amplifiers with simple kinetics for the short pulses ([[Keller fun H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (11 KB (1,644 words) - 06:33, 20 July 2020
- '''Logarithm''' is [[holomorphic function]], inverse of the [[exponential]]. [[Category:Elementary functions]]4 KB (661 words) - 10:12, 20 July 2020
- H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. [[Aequationes Mathematicae]], v.81, p.65- Abstract — The holomorphic function h is constructed such that h(h(z))=z! ; this function is interpret7 KB (1,091 words) - 23:03, 30 November 2019
- In the simple case, \(f\) is just [[holomorphic function]] of a single variable; then \(L\) is assumed to be a [[complex nu ...] offers the table of evaluations of some fixed points for some elementary functions4 KB (574 words) - 18:26, 30 July 2019
- '''Complex map''' is the graphical representation of a [[holomorphic function]] with the isolines of its real part and those of its imaginary pa For any holomorphic function, in any point, the isolines of the real part are orthogonal to tho2 KB (254 words) - 06:59, 1 December 2018
- [[Category:Holomorphic functions]]5 KB (275 words) - 07:00, 1 December 2018
- '''Holomorphic function''' is concept of the theory of functions of complex variables that refers the the existence of the derivative. Then, function \(f\) is called holomorphic on \(C\).1 KB (151 words) - 21:08, 25 January 2021
- ...proximations for the inverse function, it may have sense to consider it as holomorphic function of the complex argument. [[Category:Mathematical functions]]12 KB (1,754 words) - 18:25, 30 July 2019
- ==Relation to other special functions== According to the Axiom [[TORI]] number 6, the simplest among related functions should be considered as principal, primary. From this axiom, it follows, th27 KB (4,071 words) - 18:29, 16 July 2020
- ==Relation with other functions== '''LambertW''' is [[Holomorphic function]] at the whole complex plane except half-line along the negative p8 KB (1,107 words) - 18:26, 30 July 2019
- ...ng with real numbers. However, the difference become clearly seen is these functions are plotted in the complex plane. ...ermined by the two parameters \(P_{\rm sat}\) and \(t\) through the known functions Doya and Tania. Such a model seems to be applied, in particular, for the [[19 KB (2,778 words) - 10:05, 1 May 2021
- For a given function \(T\), called [[transfer function]], the holomorphic solution \(F\) of [[Transfer equation]] In any pair of holomorphic functions \(F\), \(G\!=\!F^{-1}\),11 KB (1,565 words) - 18:26, 30 July 2019
- Such a \(\varphi\) is assumed to be [[holomorphic function]] for some domain of values of \(z\). </ref> in the middle or 20 century. But the [[real-holomorphic]] solution was not constructed that time.5 KB (750 words) - 18:25, 30 July 2019
- Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188 For iteration of functions, the same notation is used also by [[Walter Bergweiler]]14 KB (2,203 words) - 06:36, 20 July 2020
- For example, the existence and uniqueness of the holomorphic [[tetration]] with certain properties is declared as theorem in the first p H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (2 KB (248 words) - 14:33, 20 June 2013
- Function \(\mathrm {tet}(z)\) is holomorphic in the whole complex plane except the line \(\Re(z)\le -2\). where \(\eta\) is holomorphic periodic function with period unity,14 KB (1,972 words) - 02:22, 27 June 2020
- http://www.springerlink.com/content/u712vtp4122544x4 D.Kouznetsov. Holomorphic extension of the logistic sequence. Moscow University Physics Bulletin, 201 ...t/u7327836m2850246/ H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (6 KB (312 words) - 18:33, 30 July 2019
- ...rithm, the \(J^n f\) may have singularities and cutlines even if \(f\) is holomorphic function. ...ay consider application of the fractional differentiation to some specific functions; for example, the polynomial or the exponential.9 KB (1,321 words) - 18:26, 30 July 2019
- http://www.springerlink.com/content/u712vtp4122544x4 D.Kouznetsov. Holomorphic extension of the logistic sequence. Moscow University Physics Bulletin, 201 ...t/u7327836m2850246/ H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (7 KB (381 words) - 18:38, 30 July 2019
- '''ArcCos''', or '''acos''' is [[holomorphic function]], inverse of [[cos]]. '''ArcCos''', or '''acos''', or '''arccos''' is [[holomorphic function]], inverse of [[cos]].5 KB (754 words) - 18:47, 30 July 2019