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• AuNem
  [[AuNem]] is [[Abel function]] of the [[Nemtsov function]], \(\mathrm{Nem}_q(z)=z+z^3+q z^4 ~ ~ \(G=\mathrm{Nem}_q\) is solution of the [[Abel equation]] for the transfer function \(T=\mathrm{Nem}_q\) :
  9 KB (1,441 words) - 18:45, 30 July 2019
• AuPow
  [[AuPow]] is specific [[Abelpower]] function, id est, the specific [[Abel function]] for the [[Power function]]. For \(a\!=\!2\), both functions [[AdPow]] and [[AuPow]] are shown in Fig.1
  2 KB (284 words) - 18:43, 30 July 2019
• Base e1e
  ...], [[SuperExponential]] (in particular, the [[tetration]]) and the inverse functions. ...of the [[fixed point]]s and behaviour of the [[superfunction]]s and the [[Abel function]]s are pretty different for the similar values of base \(b\) ment
  4 KB (559 words) - 17:10, 10 August 2020
• Base sqrt2
  [[Base sqrt2]] is article about functions that refer to base \(b=\sqrt{2}\). its [[superfunction]] and the corresponding [[Abel function]].
  3 KB (557 words) - 18:46, 30 July 2019
• Conjecture on superfunctions
  ...(z))=SuSin(z+1). The Abel function AuSin is constructed as solution of the Abel equation AuSin(sin(z))=AuSin(z)+1; in wide range of values z, the relation ...(z))=SuSin(z+1). The Abel function AuSin is constructed as solution of the Abel equation AuSin(sin(z))=AuSin(z)+1; in wide range of values z, the relation
  7 KB (1,031 words) - 03:16, 12 May 2021
• Eigendecomposition
  ...lgorithm for dimensions greater than 4 must either be infinite, or involve functions of greater complexity than elementary arithmetic operations and fractional
  4 KB (518 words) - 18:46, 30 July 2019
• 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
  [[Exotic iteration]] refers to the construction of [[superfunction]], the [[Abel function]] and corresponding iterates of the transfer function \(T\) at its ...of regular iteration, while the iterates are regular (id est, holomorphic) functions at least in some vicinity of the fixed point.
  11 KB (1,715 words) - 18:44, 30 July 2019
• NemBra
  ...nctions [[ArcNem]] and [[ArkNem]] gives the unnecessary cut lines of the [[Abel function]] [[Abel function]],
  4 KB (618 words) - 18:46, 30 July 2019
• NemBran
  ...ch, in its turn, necessary for evalution of function [[AuNem]], which is [[Abel function]] for the [[Nemtsov Function]]. Functions [[SuNem]] and [[AuNem]] are used to express the non-integer iterates of the
  3 KB (400 words) - 18:48, 30 July 2019
• Nembran.cin
  ...and [[ArkNem]], but namely [[ArqNem]] is required for evaluation of the [[Abel function]] [[AuNem]] of the [[Nemtsov function]].
  2 KB (281 words) - 07:03, 1 December 2018
• Nemtsov function
  ...e Nemtsov function are considered, and also some properties of the related functions: [[Abel function]], denoted with [[SuNem]],
  14 KB (2,157 words) - 18:44, 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 ( ...which solution is "best.'' We will approach the problem by first solving Abel's functional equation \(\alpha(e^x) = \alpha(x) + 1\) by perturbing the exp
  6 KB (950 words) - 18:48, 30 July 2019
• SdPow
  ...xpressed as elementary functions. For \(a\!=\!2\), these functions are who functions are shown in Fig.1.
  1 KB (202 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
  ...lation of the function to other elementary functions or with other special functions, defined earlier; even if the relation is asymptotic or approximate. ...valent of one dollar''' would be suitable in their descriptions as special functions.
  7 KB (991 words) - 18:48, 30 July 2019
• SuNem
  ...mplification of he algorithm, the precision and speed of evaluation of the functions are expected to improve a little bit. Inverse function of [[SuNem]] is function [[AuNem]], that is [[Abel function]] of the [[Nemtsov function]];
  6 KB (967 words) - 18:44, 30 July 2019
• SuPow
  The period \(P=2\pi\mathrm i / \ln(a)\) is the same for both these functions. Functions [[SuPow]] and [[SdPow]] are related with expression
  3 KB (405 words) - 18:43, 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

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