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  • Yulya function
    [[Category:Mathematical functions]] [[Category:Elementary functions]]
    12 KB (1,754 words) - 18:25, 30 July 2019
  • Tania function
    ==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, th
    27 KB (4,071 words) - 18:29, 16 July 2020
  • Doya function
    ...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
  • Table of superfunctions
    In any pair of holomorphic functions \(F\), \(G\!=\!F^{-1}\), | [[cosinus]], [[trigonometric functions]]
    11 KB (1,565 words) - 18:26, 30 July 2019
  • Square root of exponential
    ...s of the [[SuperFactorial]] and [[AbelFactorial]] (or "ArcSuperFactorial") functions. ...t/u7327836m2850246/ H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. [[Aequationes Mathematicae]], '''81''', p
    5 KB (750 words) - 18:25, 30 July 2019
  • Iteration
    Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188 XINZHI LIU. Stability of Impulsive Control Systems with Time Delay. Mathematical and Computer Modelling 39 (2004) 511-519.
    14 KB (2,203 words) - 06:36, 20 July 2020
  • Natural tetration
    The pair of functions \(\mathrm {tet}\) and \(\mathrm{ate}\) The non–integer iterations of exponential give the class of functions that grow faster than any polynomial but slower than any exponential.
    14 KB (1,972 words) - 02:22, 27 June 2020
  • Physical quantities
    ...is important), in analogy with property [[periodicity]] of functions in [[mathematical analysis]]. Each periodic process can be interpreted as [[clock]], id set,
    3 KB (464 words) - 14:33, 20 June 2013
  • Singapore 2011
    ...ed presentation and hard discussion of the superfunctions and the transfer functions of laser amplifiers (uniqueness of the superfunction, the range of applicab ...ion to the Jerome Moloney group (University of Arizona, Arizona center for mathematical science).
    8 KB (1,147 words) - 18:44, 30 July 2019
  • Квадратный корень из факториала
    ...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 ( ...vladie.pdf D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.
    6 KB (312 words) - 18:33, 30 July 2019
  • Iterated integral
    Applied Mathematical Sciences, Vol. 4, 2010, no. 21, p.1021-1032. Keith B.Oldham, Jerome Spainer. The fractional calculus. Mathematical science and engineering, Vol. 111, Academic Press 1974.
    9 KB (1,321 words) - 18:26, 30 July 2019
  • Корень из факториала
    ...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 ( ...vladie.pdf D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.
    7 KB (381 words) - 18:38, 30 July 2019
  • Fsexp.cin
    //Other functions defined below provide approximations for various parts of the complex plane ...vladie.pdf D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.
    9 KB (654 words) - 07:00, 1 December 2018
  • ArcCosc
    Four mathematical constants are defined above. In order to avoid confusions with single–let Knowledge of these constants simplifies evaluation of functions [[ArcCosc]] and [[ArcCohc]].
    8 KB (1,137 words) - 18:27, 30 July 2019
  • Wakame
    ==[[Sazae-san functions]] and related constants== ...15 decimal digits are used in the numerical implementation of the related functions.
    4 KB (581 words) - 18:25, 30 July 2019
  • Sazae-san constants
    [[File:SazaeconT.png|600px|right|thumb|Graphics of functions [[cohc]] and [[cosc]] ]] ...ma and singularities of functions [[cosc]] and [[coshc]] and their inverse functions:
    4 KB (495 words) - 18:47, 30 July 2019
  • Bessel function
    Many formulas about the Bessel functions below are borrowed from the handbook by [[Abramowirtz,Stegun]] Abramovitz, Stegun. Handbook on mathematical functions.
    13 KB (1,592 words) - 18:25, 30 July 2019
  • LogisticSequence
    While no mathematical proof of uniqueness is available, it should be assumed that the function wi ...quence and its inverse functions can be expressed in terms of [[elementary functions]],
    7 KB (886 words) - 18:26, 30 July 2019
  • WrightOmega
    Bulletin of the Americal Mathematical Society, v. 65, p.89-93 (1959). For this reason, both functions, [[Tania function]] and [[WrightOmega]] are used in [[TORI]].
    4 KB (610 words) - 10:22, 20 July 2020
  • Name of function
    ...letters (and sometimes, also [[numerical digit]]s) used to identify the [[mathematical function]]s. ...in order to distinguish it/him/her from other element of the same set. For functions, the name is especially important because it allows to denote the complicat
    6 KB (901 words) - 18:27, 30 July 2019
  • Trappmann function
    ...in the [[Mathematica]] software, all the names of the implemented special functions begin with capital letter. In this sense, \(\mathrm{Tra}=\mathrm{tra}\). As for the super functions, the capitalisation (for example, \(\mathrm{SuTra}\)) is used to separate t
    9 KB (1,320 words) - 11:38, 20 July 2020
  • Zooming equation
    G. Szekeres. Regular iteration of real and complex functions. </ref>. The non-integer iterates of various functions can be constructed also with the [[superfunction]] and [[Abel function]], c
    10 KB (1,627 words) - 18:26, 30 July 2019
  • SuTra
    Applied Mathematical Sciences, Vol. 7, 2013, no. 131, 6527 - 6541 ...n function is important example of function without [[fixed points]]. Such functions were expected to be difficult for construction of the [[fractional iterate]
    9 KB (1,285 words) - 18:25, 30 July 2019
  • File:ArcGamma.jpg
    [[Category:Mathematical functions]]
    (1,188 × 924 (156 KB)) - 08:29, 1 December 2018
  • File:OneOverFactorial.jpg
    [[Category:Mathematical functions]]
    (1,244 × 949 (276 KB)) - 17:50, 20 June 2013
  • File:B271a.png
    H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 ( D.Kouznetsov. Superexponential as special function. [[Vladikavkaz Mathematical Journal]], 2010, v.12, issue 2, p.31-45.
    (1,609 × 1,417 (506 KB)) - 08:30, 1 December 2018
  • File:Elutin1a4tori.jpg
    [[Category:Mathematical functions]]
    (922 × 914 (62 KB)) - 09:38, 21 June 2013
  • File:Expc.jpg
    The quick implementation from the [[Vladikavkaz Mathematical Journal]] D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.
    (941 × 852 (48 KB)) - 18:39, 11 July 2013
  • File:ExpIte4T.jpg
    ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188. D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.
    (1,673 × 1,673 (901 KB)) - 08:35, 1 December 2018
  • File:Plog4.png
    [[Category:Mathematical functions]]
    (307 × 432 (13 KB)) - 09:38, 21 June 2013
  • File:SazaeconT.png
    Graphics of functions [[Cohc]] and [[Cosc]]. Meanings of constants [[Sazae]], [[Tarao]], [[Fune]] [[Category:Mathematical constant]]
    (2,118 × 1,682 (216 KB)) - 09:41, 21 June 2013
  • File:Superfactocomple1.png
    [[Category:Mathematical function]] [[Category:Mathematical functions]]
    (706 × 706 (172 KB)) - 00:10, 29 February 2024
  • File:Tet10bxr.jpg
    [[Category:Mathematical functions]]
    (2,491 × 1,952 (236 KB)) - 08:53, 1 December 2018
  • File:Tetreal10bx10d.png
    [[Category:Mathematical functions]]
    (2,192 × 2,026 (436 KB)) - 13:56, 5 August 2020
  • File:Tetreal2215.gif
    [[Category:Mathematical functions]]
    (876 × 881 (111 KB)) - 09:38, 21 June 2013
  • Orwell1984
    ...t and intricate that you could lose yourself in them as in the depths of a mathematical problem — delicate pieces of forgery in which you had nothing to guide yo ...It was still true that men were not equal in their native talents and that functions had to be specialized in ways that favoured some individuals against others
    587 KB (105,318 words) - 13:23, 7 April 2023
  • Algebra of generalized functions
    [[Algebra of one-dimensional generalized functions]] by [[Yurii Shirokov]] appears in but the main ideas of the non–commutative generalized functions still need to be applied in the [[Filed Theory]].
    38 KB (6,232 words) - 18:46, 30 July 2019
  • Nori
    ...justed parameters. (Here, \(M_2\) is not an adjusting parameter, but exact mathematical constant). Similar goal can be formulated for the numerical implementation ...tegration. This observation caused the need to perform certain analysis of functions [[mori]], [[nori]], [[naga]] and [[maga]].
    13 KB (1,759 words) - 18:45, 30 July 2019
  • Superpower
    The two real-holomorphic superpower functions are considered here: For \(a\!=\!2\), the explicit plots of these two functions are shown in figure 1 at right.
    6 KB (903 words) - 18:44, 30 July 2019
  • RAS reform
    ...d be stripped of their property rights, transferring the property managing functions to a federal agency that would be specially created for this purpose.</i> ...d be stripped of their property rights, transferring the property managing functions to a federal agency that would be specially created for this purpose. ..</i
    15 KB (1,750 words) - 18:44, 30 July 2019
  • Conjugation
    [[Conjugation]] is certain type of transformation of mathematical objects. This applies both to functions and to numbers.
    6 KB (921 words) - 18:46, 30 July 2019
  • Mathematical notations
    ...to describe the theoretical values of a physical quantity. In this manner, mathematical notation serves as a common language for expressing ideas and results acros ...ers e and <math>\pi</math>, etvetera. Such names form the basics of the '''mathematical notations'''.
    5 KB (753 words) - 18:47, 30 July 2019
  • File:Exp1mapT200.jpg
    ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188. D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.
    (2,281 × 1,179 (1.14 MB)) - 12:37, 28 July 2013
  • File:Exp09mapT200.jpg
    ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188. D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.
    (2,281 × 1,179 (1.23 MB)) - 12:28, 28 July 2013
  • Iterate of exponential
    Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188. Both, tet and ate are holomorphic functions; so, the representation above can be used for non-integer \(n\). The expone
    7 KB (1,161 words) - 18:43, 30 July 2019
  • File:Exm01mapT200.jpg
    The complex double implementations [[FSEXP]] and [[FSLOG]] of these functions are used in the [[C++]] code below. ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188.
    (2,281 × 1,179 (834 KB)) - 12:52, 28 July 2013
  • File:Exm05mapT200.jpg
    ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188. D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.
    (2,281 × 1,179 (705 KB)) - 12:54, 28 July 2013
  • File:Exm09mapT200.jpg
    ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188. D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.
    (2,281 × 1,179 (560 KB)) - 12:56, 28 July 2013
  • File:Exm1mapT200.jpg
    ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188. D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.
    (2,281 × 1,179 (544 KB)) - 12:47, 28 July 2013
  • Iterate of linear fraction
    All functions \(P\), \(t^n\) and \(Q\) are defined above, and \(f^n\) is expressed in a w ...nction]] and the [[Abel function]] can be expressed in terms of elementary functions. For many cases, instead of to express the [[superfunction]] through the it
    13 KB (2,088 words) - 06:43, 20 July 2020

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