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- ....Stegun: Handbook of Mathematical Functions. 6. Gamma Function and Related Functions (2010) ...r <math>z</math>, the integral can be expressed in terms of the elementary functions.27 KB (3,925 words) - 18:26, 30 July 2019
- such that, at least for \(b\!>\!1\), is holomorphic at least in \(\{ z \in \mathbb C : \Re(z)\!>\!-2\}\). H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (21 KB (3,175 words) - 23:37, 2 May 2021
- ...Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (2011)</ref> is holomorphic solution \(F(z)={\rm tet}_b(z)\) of the equations ...map of this function may be interpreted as a hint that the tetrational is holomorphic not only being considered as function of \(z\) at fixed \(b\), but also as14 KB (2,275 words) - 18:25, 30 July 2019
- In particular, the [[Ackernann functions]] and [[tetration]] can be interpreted in terms of [[superfunction]]s. ...ns came from the application to the evaluation of fractional iterations of functions.25 KB (3,622 words) - 08:35, 3 May 2021
- [[File:Penplot.jpg|300px|thumb|\(y=\mathrm{pen}(x)\) and related functions.]] ...[hexation]]. The fixed points of pentation are complex, so, for the real–holomorphic superpentation, the method of the [[Cauchi integral]] can be applied, the s7 KB (1,090 words) - 18:49, 30 July 2019
- It is assumed, that \(h\) is [[holomorphic function]] al least in some vicinity of [[halfline]] along the [[real axis] ...y, even the non-integer (and even complex) [[iteration]] of almost every [[holomorphic function]].13 KB (1,766 words) - 18:43, 30 July 2019
- The holomorphic extension of \(h\) is suggested. The holomorphic extension \(F\) of the sequence, generated with such a transfer function, i5 KB (798 words) - 18:25, 30 July 2019
- ...rate''' refer to the [[fractional iterate]] a holomorphic function that is holomorphic in vicinity it its fixed point </ref>. In general, a holomorphic function may have several fixed points, and the fractional iterates, regula20 KB (3,010 words) - 18:11, 11 June 2022
- That publication defined the \(\sqrt{!\,}\) as holomorphic function, ...roduct, the [[SuperFunction]] of Factorial and that for some other special functions are considered there.18 KB (2,278 words) - 00:03, 29 February 2024
- '''Transfer equation''' is relation between some [[holomorphic function]] \(h\), called [[transfer function]] and another function \(F\), ...vial. This determined the interest to the superfunctions from the set of [[holomorphic function]]s of [[complex variable]].3 KB (519 words) - 18:27, 30 July 2019
- [[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