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  • In [[mathematics]], the '''factorial''' is the [[meromorphic function]] with fast growth along the real axis; fo Frequently, the [[postfix]] notation <math>n!</math> is used for the factorial of number <math>n</math>.
    27 KB (3,925 words) - 18:26, 30 July 2019
  • H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, ...orialQexp.jpg|400px|right|thumb|Complex maps of functions [[square root of factorial]], left, and \(\sqrt{\exp}\), right.]]
    14 KB (2,275 words) - 18:25, 30 July 2019
  • [[Image:Sqrt(factorial)LOGOintegralLOGO.jpg|200px]]<small> [[Superfunction]]s and their inverse functions ([[Abel function]]s) allow evaluation of not only minus-first power of a function (
    25 KB (3,622 words) - 08:35, 3 May 2021
  • [[Square root of factorial]] (half-iteration of [[Factorial]]), or \(\sqrt{!\,}\) is solution \(h\) of equation \(h(h(z))=z!\). ...some vicinity of [[halfline]] along the [[real axis]], \(h\circ h=\mathrm{Factorial}\). It is assumed that \(z\!=\!2\) is [[regular point]] of \(\sqrt{!\,}(z)
    13 KB (1,766 words) - 18:43, 30 July 2019
  • In 1824, [[Niels Henrik Abel]] proved the theorem: http://www.cds.caltech.edu/~nair/abel.pdf
    2 KB (320 words) - 18:25, 30 July 2019
  • ...al iterate]] of any function $~T~$ through its [[Superfunction]] and the [[Abel function]] is considered as principal, as it allows to deal with functions </ref>, the superfunction of [[factorial]]
    20 KB (3,010 words) - 18:11, 11 June 2022
  • '''SuperFactorial''', or "superfactorial" is [[superfunction]] of [[factorial]] constructed at its [[fixed point]] 2. : \(\mathrm{SuperFactorial}(z)=\mathrm{Factorial}^z(3)\)
    18 KB (2,278 words) - 00:03, 29 February 2024
  • ==Abel function and Abel equation== .... Within some domain \(D\in \mathbb C\), the Abel function satisfies the [[Abel equation]]
    3 KB (519 words) - 18:27, 30 July 2019
  • For some given [[Transfer function]] \(T\), the '''Abel function''' \(G\) is [[inverse function]] of the corresponding [[superfunct The [[Abel equation]] relates the [[Abel function]] \(G\) and the [[transfer function]] \(T\):
    4 KB (547 words) - 23:16, 24 August 2020
  • In [[TORI]], the term usually refers to the [[Transfer equation]], the [[Abel equation]]; the transfer function is assumed to be given function that appe ...nal restrictions should be applied to make the [[superfunction]] and the [[Abel function]] unique
    11 KB (1,644 words) - 06:33, 20 July 2020
  • ...ction \(f\) can be expressed through the [[superfunction]] \(F\) and the [[Abel function]] \(G=F^{-1}\): The [[square root of factorial]], that is used as [logo]] of the Physics department of the Moscow State Un
    3 KB (438 words) - 18:25, 30 July 2019
  • [[ArcTetration]] is [[Abel function]] of the [[exponential]]. The ArcTetration satisfies the [[Abel equation]]
    7 KB (1,091 words) - 23:03, 30 November 2019
  • ...mentations for [[tetration]], [[ArcTetration]], [[SuperFactorial]], [[Abel Factorial]], etc.; of order of a dozen coefficients of the asymptotic expansion can b
    12 KB (1,901 words) - 18:43, 30 July 2019
  • ...on]], the [[ArcTania]] function is the [[Abel function]], satisfying the [[Abel equation]] ...09supefae.pdf D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Moscow University Physics Bulletin, 2010, v.65, No.1, p.6-12.
    19 KB (2,778 words) - 10:05, 1 May 2021
  • ...1}\) is called [[Abel function]] with respect to \(T\); it satisfies the [[Abel equation]] function \(G\) can be declared as [[Abel function]], and then the corresponding [[transfer function]]
    11 KB (1,565 words) - 18:26, 30 July 2019
  • ...function \(T\) through its [[superfunction]] \(F\) and the corresponding [[Abel function]] \(G=F^{-1}\): ...rfunction]] and the [[Abel function]], and similarly, the [[square root of factorial]]
    5 KB (750 words) - 18:25, 30 July 2019
  • ...FacIteT.jpg|400px|thumb|Fig.2. Iterates of [[Factorial]]: \(~y\!=\!\mathrm{Factorial~}^{~n}(x)~\) for various \(n\)]] <ref name="factorial">
    14 KB (2,203 words) - 06:36, 20 July 2020
  • ...for tetrations to other values of baze and for other funcitons, including factorial and polunomials. \( p\!+\!\mathrm i q=\varphi(z) \) <ref name="factorial">
    14 KB (1,972 words) - 02:22, 27 June 2020
  • : \(\sqrt{\,!\,}(х)=\mathrm{Factorial}^{1/2}(x)\)
    6 KB (312 words) - 18:33, 30 July 2019
  • Корень из факториала ([[square root of factorial]]) – это такая функция \(h\), что ...xt.pdf?page=1 D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Moscow University Physics Bulletin, 2010, v.65, No.1, p.6-12
    7 KB (381 words) - 18:38, 30 July 2019
  • ...ered as a serious obstacle at the building-up its [[superfunction]], the [[Abel function]] and the non–integer [[iterate]]s of function Tra. According to the general statement by <ref name="factorial">
    9 KB (1,320 words) - 11:38, 20 July 2020
  • ...various functions can be constructed also with the [[superfunction]] and [[Abel function]], considering the [[transfer equation]] instead of the [[zooming D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Moscow University Physics Bulletin, 2010, v.65, No.1, p.6-12. (Russian ver
    10 KB (1,627 words) - 18:26, 30 July 2019
  • D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Moscow University Physics Bulletin, 2010, v.65, No.1, p.6-12. (Russian ver ...e function of SuTra, id est, [[AuTra]]\(=\)SuTra\(^{-1}\), satisfies the [[Abel equation]]
    9 KB (1,285 words) - 18:25, 30 July 2019
  • ...Fac]], id est, ([[ArcSuperFactorial]]), id est, the [[Abel function]] of [[Factorial]]. In wide ranges of values of z, \(\rm AuFac(Sufac(z))\!=\!z~\) and \(~\rm ...lFactorial]] [[Category:Factorial]] [[Category:SuperFactorial]] [[Category:Abel function]] [[Category:C++]]
    2 KB (137 words) - 18:46, 30 July 2019
  • The Abel function (or abelfunction) is the inverse of superfunction, \(G=F^{-1}\) The abelfunction is solution of the Abel equation
    15 KB (2,166 words) - 20:33, 16 July 2023
  • ...her solution of the [[transfer equation]], nor that of the corresponding [[Abel equation]] is unique. The additional conditions are required to evaluate th ...ontent/u7327836m2850246/ H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81,
    10 KB (1,534 words) - 06:44, 20 July 2020
  • ...(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 D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Moscow University Physics Bulletin, 2010, v.65, No.1, p.6-12. (Russian ver
    7 KB (1,031 words) - 03:16, 12 May 2021
  • D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Moscow University Physics Bulletin, 2010, v.65, No.1, p.6-12. (Russian ver ==Abel function of sin==
    15 KB (2,314 words) - 18:48, 30 July 2019
  • ...мула (7.28)|| \(\displaystyle F(z)=\lim_{n\rightarrow \infty} \mathrm{Factorial|}^n(\tilde F(z\!-\!n))\) || \(\displaystyle F(z)=\lim_{n\rightarrow \infty} ...4, последний абзац|| что \(\mathrm {SuFac}(3)\!=\!\mathrm{Factorial}^z(3)\) и, соответственно, || что
    19 KB (1,132 words) - 20:36, 16 July 2023
  • functions: for factorial by <ref name="fac"> D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial.
    15 KB (2,392 words) - 11:05, 20 July 2020