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• Conjecture on superfunctions
  ...of function sin are considered. The superfunction SuSin is constructed as holomorphic solution of the transfer equation sin(SuSin(z))=SuSin(z+1). The Abel functi D.Kouznetsov. Holomorphic extension of the logistic sequence. Moscow University Physics Bulletin, 201
  7 KB (1,031 words) - 03:16, 12 May 2021
• Elementary function
  ...ion of the first three [[Ackermann function]]s functions and their inverse functions. The first three ackermann functions are
  3 KB (496 words) - 18:45, 30 July 2019
• Exotic iteration
  ...of regular iteration, while the iterates are regular (id est, holomorphic) functions at least in some vicinity of the fixed point. ...ation''' or '''singular iteration''' could be also used to define the same functions.
  11 KB (1,715 words) - 18:44, 30 July 2019
• Gauss-Laguerre quadrature
  ...\, \exp(-x)\) is integrand, \(f\) is supposed to be smooth (and preferably holomorphic) function, ...efficient in the numerical calculations with approximation of atomic wave functions in spherical coordinates.
  7 KB (997 words) - 18:44, 30 July 2019
• Inverse function
  ==Self-inverse functions== Some functions are their own inverse function.
  3 KB (444 words) - 18:43, 30 July 2019
• Kori
  Kori is [[entire function]], it is holomorphic in the whole complex plane. The zero in the denominator in the definition i ...escription and implementation of functions [[kori]] and some other related functions ([[maga]], [[mori]], [[naga]], [[nori]]) appear as [[tool]]s for the descri
  14 KB (1,943 words) - 18:48, 30 July 2019
• Lof
  ...function \(~z\! \mapsto\! \ln\!\big(\)[[Factorial]]\((z)\big)~\) , that is holomorphic in the most of the complex \(z\) plane (except \(z\!\le\!-1\)). ...aginary part of the argument, it is, indeed, just combination of these two functions.
  3 KB (478 words) - 18:43, 30 July 2019
• Maga
  ...jpg|300px|thumb|\(y\!=\!\mathrm{maga}(x)\) (thick black curve) and related functions]] ...the complex plane. For the last option, the holomorphic properties of the functions involved (and their complex maps) should be analysed.
  8 KB (1,256 words) - 18:44, 30 July 2019
• Naga
  ...simple combination of the [[Bessel function]] [[BesselJ0]] with elementary functions: ==Relation with other functions==
  5 KB (750 words) - 10:00, 20 July 2020
• NemBra
  [[NemBra]] is holomorphic function that expresses values of the [[Nemtsov function]] while two other its inverse functions [[ArcNem]] and [[ArkNem]] gives the unnecessary cut lines of the [[Abel fun
  4 KB (618 words) - 18:46, 30 July 2019
• NemBran
  ...l \(q\) is presented. For real \(q\) function \(\mathrm{Nem}_q\) is real–holomorphic, id est, \(\mathrm{Nem}_q(z^*)=\mathrm{Nem}_q(z)^*\); this simplifies the c Functions [[SuNem]] and [[AuNem]] are used to express the non-integer iterates of the
  3 KB (400 words) - 18:48, 30 July 2019
• Nemtsov function
  ...e Nemtsov function are considered, and also some properties of the related functions: ...versions had been assigned (designated) the different names. These inverse functions have different positions of the cuts of the range of holomorphism.
  14 KB (2,157 words) - 18:44, 30 July 2019
• Pentation
  The additional condition, common for all ackermann functions is assumed, Pentation is holomorphic at least in the part of the complex plane, while the real part of the argum
  5 KB (803 words) - 18:48, 30 July 2019
• Pluralism
  H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 ( ...xponential function so as to produce a real fixed point, allowing a unique holomorphic solution. We then use this solution to find a solution to the unperturbed
  6 KB (950 words) - 18:48, 30 July 2019
• Sin
  The postulating of some properties of some functions may have sense while no proof is available. Properties of functions [[sin]] and [[cos]], can be deduced from the differential equation above. A
  4 KB (680 words) - 18:43, 30 July 2019
• Special function
  ...ay of evaluation of the function. In the most of cases, this refers to a [[holomorphic function]] of a single complex variable. ...lation of the function to other elementary functions or with other special functions, defined earlier; even if the relation is asymptotic or approximate.
  7 KB (991 words) - 18:48, 30 July 2019
• SuSin
  ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188</ref>. SuSin can be aproximated with elementary functions.
  15 KB (2,314 words) - 18:48, 30 July 2019
• Nemtsov function and its iterates
  G. Szekeres. Regular iteration of real and complex functions. Acta Mathematica, September 1958, Volume 100, Issue 3, pp 203-258. W.Bergweiler. Iteration of meromorphic functions. Bulletin (New Series) of the American Mathematical society, v.29, No.2 (19
  15 KB (2,392 words) - 11:05, 20 July 2020
• Shell-Thron region
  H.Trappmann, D.Kouznetsov. Uniqueness of holomorphic Abel functions at a complex fixed point pair Aequationes Mathematicae, v.81, p.65-76 (2011
  7 KB (1,082 words) - 07:03, 13 July 2020
• Smooth superation
  Assume, some holomorphic function \( f \) is given. Consider holomorphic function \(a \) of two variables such that
  3 KB (341 words) - 21:45, 21 June 2020

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