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  • Mathematics of Computation
    [[Mathematics of Computation]] ([[MOC]]) is [[Scientific journal]] dedicated to numerical analysis, computational discrete mathematics, number theory, algebra, combinatorics, and related fields.
    2 KB (344 words) - 07:02, 1 December 2018

Page text matches

  • Logic
    <b>Logic</b> is part of mathematics that deals with Boolean algebra. This algebra deals with logical variables. Creation of logics is usually attributed to [[George Bool]]
    8 KB (1,403 words) - 14:24, 20 June 2013
  • Tetration
    is the \(\mathbb C \mapsto \mathbb C\) function, which is solution of equations ...n]] of [[exponential]] to base \(b\). Exponential is [[transfer function]] of tetration.
    21 KB (3,175 words) - 23:37, 2 May 2021
  • Mapping
    ...space to itself or to another space, and also the graphical representation of such a function. Such a representation is called '''map'''. ...surface of the Earth (or that of another planet) is mapped to the surface of
    14 KB (2,275 words) - 18:25, 30 July 2019
  • Superfunction
    [[Superfunction]] comes from iteration of some function. ...derbrace{T\Big(T\big(... T(t)...\big)\Big)}} \atop {z \mathrm{~evaluations~of~function~}T\!
    25 KB (3,622 words) - 08:35, 3 May 2021
  • Natural pentation
    [[Natural pentation]] is [[supefrunction]] of [[natural tetration]] tet; [[natural pentation]] satisfies the [[transfer e ...atural tetration]], which is solution \(L=L_0\approx -1.8503545290271812\) of equation \(\mathrm{tet}(L)=L\).
    7 KB (1,090 words) - 18:49, 30 July 2019
  • Place of science in the human knowledge
    [[Place of Science in the Human Knowledge]] ([[Place of science in the human knowledge]])
    100 KB (14,715 words) - 16:21, 31 October 2021
  • Место науки в человеческом знании
    ..." style="float:right;width:246px"><div style="width:260px"><small>Examples of things considered as [[science]]:</small> [[Complex map]] of function [[AuSin]]</small> !-->
    111 KB (2,581 words) - 16:54, 17 June 2020
  • Square root of factorial
    ...l]] (half-iteration of [[Factorial]]), or \(\sqrt{!\,}\) is solution \(h\) of equation \(h(h(z))=z!\). ...=\mathrm{Factorial}\). It is assumed that \(z\!=\!2\) is [[regular point]] of \(\sqrt{!\,}(z)\), and
    13 KB (1,766 words) - 18:43, 30 July 2019
  • Holomorphic extension of the Collatz subsequence
    Terras, R. "On the Existence of a Density." Acta Arith. 35, 101-102, 1979. is subsequence of the [[Collatz sequense]]
    5 KB (798 words) - 18:25, 30 July 2019
  • Regular Iteration
    A [[fractional iterate]] $\phi$ of an analytic function $f$ at fixpoint $a$ is called regular, iff $\phi$ is a ...ait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.
    20 KB (3,010 words) - 18:11, 11 June 2022
  • SuperFactorial
    '''SuperFactorial''', or "superfactorial" is [[superfunction]] of [[factorial]] constructed at its [[fixed point]] 2. Here, the upper index of a function indicates the number of [[iteration]]s.
    18 KB (2,278 words) - 00:03, 29 February 2024
  • Abel function
    ...er function]] \(T\), the '''Abel function''' \(G\) is [[inverse function]] of the corresponding [[superfunction]] \(F\), id est, \(G=F^{-1}\). In certain range of values of \(z\), this equation is equivalent of the [[Transfer equation]]
    4 KB (547 words) - 23:16, 24 August 2020
  • Transfer function
    [[File:KellerDoyaT.png|300px|thumb|Transfer functions of laser amplifiers with simple kinetics for the short pulses ([[Keller functi ...ion of the state of the system in terms of its state at the precedent step of evolution.
    11 KB (1,644 words) - 06:33, 20 July 2020
  • Japan
    [[File:Japan.gif|320px]] Map of Japan by [[CZ]]<ref name="CZpic">http://en.citizendium.org/wiki/Japan</ref> ...日本 , にほん)　is country in the Pacific Ocean, near the East side of Asia,
    15 KB (2,106 words) - 13:37, 5 December 2020
  • ArcTetration
    [[ArcTetration]] \( \mathrm{ate} \) is inverse function of [[tetration]] .... Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation 78 (2009), 1647-1670.
    7 KB (1,091 words) - 23:03, 30 November 2019
  • Fixed point
    [[File:Tet5loplot.jpg|400px|thumb|Graphical search for the [[fixed point]]s of [[tetration]]; \(y\!=\!\mathrm{tet}_b(x)\) versus \(x\) for various \(b\) ] For a given function \(f\), the '''fixed point''' is solution \(L\) of equation
    4 KB (574 words) - 18:26, 30 July 2019
  • Mathematica
    ...upports this language, developed by the [[Wolfram corporation]] in the end of century 20 for ...ation of functions, plotting graphics and other things that require some [[mathematics]].
    12 KB (1,901 words) - 18:43, 30 July 2019
  • Doya function
    The [[Doya function]] and its iterates appear as the [[transfer function]] of an [[optical amplifier]] with simplest kinetic model. In vicinity of the real axis (While \(|\Im(z)| \!<\! \pi\)), the [[Doya function]] can be
    19 KB (2,778 words) - 10:05, 1 May 2021
  • Table of superfunctions
    ...nction \(T\), called [[transfer function]], the holomorphic solution \(F\) of [[Transfer equation]] In any pair of holomorphic functions \(F\), \(G\!=\!F^{-1}\),
    11 KB (1,565 words) - 18:26, 30 July 2019
  • Square root of exponential
    ...root of exponential]] \(\varphi=\sqrt{\exp}=\exp^{1/2}\) is half-iteration of the [[exponential]], id est, such function that its second iteration gives ...rphi\) is assumed to be [[holomorphic function]] for some domain of values of \(z\).
    5 KB (750 words) - 18:25, 30 July 2019
  • Iteration
    [[File:PowIteT.jpg|400px|thumb|Fig.1. Iterates of \(T(z)=z^2~\): \(~y\!=\!T^n(x)\!=\!x^{2^n}~\) for various \(n\)]] [[File:FacIteT.jpg|400px|thumb|Fig.2. Iterates of [[Factorial]]: \(~y\!=\!\mathrm{Factorial~}^{~n}(x)~\) for various \(n\)]
    14 KB (2,203 words) - 06:36, 20 July 2020
  • Theorem
    ...usually referring to [[mathematics]], that is proved baser on certain set of axioms. For example, the existence and uniqueness of the holomorphic [[tetration]] with certain properties is declared as theore
    2 KB (248 words) - 14:33, 20 June 2013
  • Natural tetration
    ...\) is assumed; the tetration approaches the fixed points \(L\) and \(L\)^* of exponential. Existence of natural tetration been indicated in 1950 by [[Hellmuth Kneser]] in 1950
    14 KB (1,972 words) - 02:22, 27 June 2020
  • Квадратный корень из факториала
    ...нглийской версии этой статьи, см. [[Square root of factorial]].
    6 KB (312 words) - 18:33, 30 July 2019
  • Корень из факториала
    Корень из факториала ([[square root of factorial]]) – это такая функция \(h\), что ...amlib.ru/img/g/garik/dubinushka/index.shtml Logo of the Physics Department of the Moscow State University. (In Russian);
    7 KB (381 words) - 18:38, 30 July 2019
  • Filog
    [[File:Filogbigmap100.png|400px|right|thumb|[[Complex map]] of Filog; \(u\!+\! \mathrm i v=\mathrm{Filog}(x\!+\! \mathrm i y)\) ]] ...t|thumb|\(u\!+\! \mathrm i v=\mathrm{Filog}(x\!+\! \mathrm i y)\), zoom in of the central part ]]
    4 KB (572 words) - 20:10, 11 August 2020
  • Tetration to Sheldon base
    [[File:Shelre60.png|500px]]<small> Explicit plot of real and imaginary parts of tetration to base \(b\!=\!s\)</small> [[File:Shelima600.png|500px]]<small>Distribution of tetration to \(b\!=\!s\) along the imaginary axis</small>
    5 KB (707 words) - 21:33, 13 July 2020
  • GLxw2048.inc
    '''GLxw2048.inc''' is text file, containing nodes and weights of the ...update to another number of points is straightforward. For moderate number of nodes (maximum 32), the
    108 KB (1,626 words) - 18:46, 30 July 2019
  • Iterated Cauchi
    '''Iterated Cauchi''' is algorithm of iterative solution of the [[Transfer equation]] \(U=T^{-1}\) is also holomorphic in the working range of valies.
    6 KB (987 words) - 10:20, 20 July 2020
  • Bessel transform
    '''WARNING!''' The formulas of this article are not yet verified with pics, In publications, it is difficult to see difference between meanings of terms '''Hankel transform''' and '''Bessel transform''' is found. In TORI,
    8 KB (1,183 words) - 10:21, 20 July 2020
  • F45E.cin
    // [[F45E.cin]] is routine for evaluation of the [[superfunction]] of the [[exponential]] to base \(b\!=\!\sqrt{2}\), constructed at the fixed po ...ait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, v.271, July 2010, p.1727-1756.
    1 KB (139 words) - 18:48, 30 July 2019
  • F45L.cin
    // [[F45E.cin]] is routine for evaluation of the [[Abel function]] of the [[exponential]] to base \(b\!=\!\sqrt{2}\), constructed at the fixed po ...ait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, v.271, July 2010, p.1727-1756.
    2 KB (163 words) - 18:47, 30 July 2019
  • ArcLambertW
    One of the inverse function of [[ArcLambertW]] is called [[LambertW]] In wide ranges of values of \(z\), the relations
    3 KB (499 words) - 18:25, 30 July 2019
  • SuZex
    [[SuZex]] is [[superfunction]] of [[ArcLambertW]], denoted also as [[zex]], \(\mathrm{zex}(z)=z \exp(z)\). The [[explicit plot]] of function [[SuZex]] is shown in Figure 1 in comparison with that function [[
    7 KB (1,076 words) - 18:25, 30 July 2019
  • AuZex
    [[File:AuZexLamPlotT.jpg|620px|thumb|Fig.1. Plot of [[AuZex]] (thick curve) in comparison to [[LambertW]] (thin curve) ]] [[Auzex]] is inverse function of [[SuZex]]; \(\mathrm{AuZex} = \mathrm{SuZex}^{-1}\)
    6 KB (899 words) - 18:44, 30 July 2019
  • Zooming equation
    at least in some vicinity of zero, and \(~K\!=\!T'(0)~\). Function \(~f~\) is requested to built-up. ...scribes the variation of value of function \(~f~\) at the scaling, zooming of its argument with factor \(~K~\).
    10 KB (1,627 words) - 18:26, 30 July 2019
  • File:B271a.png
    [[Complex map]] of [[ArcTetration]] to base $\mathrm e \approx 2.71~$: ...nchpoints $L\!\approx \! 0.2+1.3 \mathrm i$ and $L^*$ are [[fixed point]]s of [[logarithm]].
    (1,609 × 1,417 (506 KB)) - 08:30, 1 December 2018
  • File:B271t.png
    ...p]] of tetration to base $\mathrm e$, isolines of real and imaginary parts of ==C++ generator of curves==
    (1,609 × 1,417 (791 KB)) - 08:30, 1 December 2018
  • File:E1efig09abc1a150.png
    [[Complex map]]s of [[tetration]] $\mathrm{tet}_b$ to base<br> ...on of the Two Regular Super-Exponentials to base exp(1/e). (Mathematics of Computation, 2011, in press)
    (2,234 × 711 (883 KB)) - 08:34, 1 December 2018
  • File:Esqrt2iterMapT.png
    [[Complex map]] of 1/3 th iteration of the [[exponential]] to [[base sqrt(2)]]. ...ait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, v.271, July 2010, p.1727-1756.</ref>,
    (1,092 × 1,080 (1.36 MB)) - 09:43, 21 June 2013
  • File:ExpQ2mapT.png
    [[Complex map]] of [[exponential]] to [[base sqrt2]], id est, $b=\sqrt{2}$; ...ion to base sqrt(2)]] in the illustration of the application of the method of [[regular iteration]] to construct the [[superfunction]]
    (1,765 × 1,729 (1.15 MB)) - 08:35, 1 December 2018
  • File:ExpQ2plotT.png
    [[Explicit plot]] of [[exponential]] to base $b\!=\!\sqrt{2} \approx 1.414213562373095$ The [[fixed point]]s $L\!=\!2$ and $L\!=\!4$ are solutions of the equation
    (2,512 × 1,744 (175 KB)) - 08:35, 1 December 2018
  • File:Filogbigmap100.png
    [[File:Filogmap300.png|right|300px|thumb|The zoom-in of the central part of the map]] [[Complex map]] of function [[Filog]].
    (2,870 × 2,851 (847 KB)) - 08:36, 1 December 2018
  • File:Filogmap300.png
    [[Complex map]] of function [[Filog]]. ==Semantics of Filog==
    (893 × 897 (292 KB)) - 09:40, 21 June 2013
  • File:IterEq2plotU.png
    ...f [[exponential]] to [[base sqrt(2)]] for various values of the number $c$ of iterations. ...ion, the plotter uses the implementation through the [[superfunction]] $F$ of the exponential to base $\sqrt{2}$, constructed at the fixed point $L\!=\!4
    (2,944 × 2,944 (986 KB)) - 21:42, 27 September 2013
  • File:LogQ2mapT2.png
    [[Complex map]] of [[logarithm]] to base $b\!=\!\sqrt{2}$; The cut of the range of holomorphism is marked with dashed line. Lines $u\!=\!1$, $u\!=\!2$, $u\!=\
    (1,765 × 1,729 (1.43 MB)) - 09:43, 21 June 2013
  • File:SqrtExpZ.jpg
    [[Complex map]]s of function <math>f=\exp^c(z)</math> in the <math>z</math> plane for some real values of <math>c=\pm 1, \pm 0.9, \pm 0.5, \pm 0.1</math>.
    (842 × 953 (83 KB)) - 11:56, 21 June 2013
  • File:Sqrt2figf45bT.png
    [[Complex map]] of the primary expansion of the growing [[superexponential]] to base $b\!=\!\sqrt{2}$ built up at the [ :$a_0=L=4$ is fixed point of the exponential transfer function $T$,
    (2,180 × 2,159 (1.01 MB)) - 08:52, 1 December 2018
  • File:Sqrt2figf45eT.png
    [[Complex map]] of the real-holomorphic [[superfunction]] $F$ of the [[exponential]] to base $b\!=\!\sqrt{2}$ built up at its fixed point $L ...is almost Figure 2 (left at the bottom) of publication in [[Mathematics of Computation]]
    (2,180 × 2,159 (1.18 MB)) - 08:52, 1 December 2018
  • File:Sqrt2figL45eT.png
    [[Complex map]] of the [[Abel function]] $G$ of the [[exponential]] to base $b\!=\!\sqrt{2}$ constructed at the fixed point In the [[Mathematics of computation]]
    (2,180 × 2,159 (1.07 MB)) - 12:53, 20 July 2020
  • File:TetSheldonImaT.png
    The holomorphic solution $F$ of equation where [[Filog]] is [[fixed point]] of the [[logarithm]].
    (4,359 × 980 (598 KB)) - 09:40, 21 June 2013
  • Maps of tetration
    ...e [[complex map]]s of [[tetration]] \(\mathrm{tet}_b\) to different values of base \(b\). For real values of base \(b\), the real-real plots \(y\!=\!\mathrm{tet}_b(x)\) are shown in th
    5 KB (761 words) - 12:00, 21 July 2020
  • Интегральная формула Коши
    ...2009). Solutions of F(z+1)=exp(F(z)) in the complex plane.. Mathematics of Computation, 78: 1647-1670. While Russian version of that article, id est, [[Тетрация]] is not loaded, the English vers
    16 KB (821 words) - 14:42, 21 July 2020
  • Iterate of exponential
    ...function \(f(z)=\exp^n(z)\), where upper superscript indicates the number of iteration. ...the number in superscript after a name of any function denotes the number of iteration. This notation is neither new, nor original;
    7 KB (1,161 words) - 18:43, 30 July 2019
  • Iterate of linear fraction
    [[Iterate_of_linear_fraction]] (or [[iteration of linnet friaction]]) refers to function [[Iterate]] of a [[linear fraction]] can be expressed with also some linear fraction. This
    13 KB (2,088 words) - 06:43, 20 July 2020
  • Superfunctions
    ...of [[abelfunction]]s, [[superfunction]]s, and the non-integer [[iterate]]s of holomorphic functions. In particular, results for [[tetration]], [[arctetration]] and [[iterate]]s of [[exponential]] are presented.
    15 KB (2,166 words) - 20:33, 16 July 2023
  • File:IterEq2plotT.jpg
    ...f [[exponential]] to [[base sqrt(2)]] for various values of the number $c$ of iterations. ...ion, the plotter uses the implementation through the [[superfunction]] $F$ of the exponential to base $\sqrt{2}$, constructed at the fixed point $L\!=\!4
    (2,922 × 2,922 (1.35 MB)) - 08:38, 1 December 2018
  • File:Ack3a600.jpg
    [[Complex map]] of [[tetration]] to base $b\!=\!\sqrt{2}\!\approx\!1.41$ ==[[C++]] Generator of map]==
    (5,130 × 1,793 (1.09 MB)) - 08:28, 1 December 2018
  • File:Ack3b600.jpg
    [[Complex map]] of [[tetration]] to base $b\!=\!\exp(1/\mathrm e)\!\approx\!1.44$ ==[[C++]] Generator of map]==
    (5,130 × 1,776 (1 MB)) - 08:28, 1 December 2018
  • File:Ack3c600.jpg
    [[Complex map]] of [[tetration]] to base $b\!=\!3/2\!=1.5$ ==[[C++]] Generator of map]==
    (5,130 × 1,776 (1.5 MB)) - 08:28, 1 December 2018
  • File:Ack4a600.jpg
    [[Complex map]] of [[tetration]] to base $b\!=\!2$ ==[[C++]] Generator of map==
    (5,130 × 1,776 (1.65 MB)) - 11:57, 21 July 2020
  • File:Ack4aFragment.jpg
    Fragment of image http://mizugadro.mydns.jp/t/index.php/File:Ack4a600.jpg [[Complex map]] of [[tetration]] to base $b\!=\!2$
    (3,457 × 1,776 (1.63 MB)) - 08:28, 1 December 2018
  • File:Ack4b600.jpg
    [[Complex map]] of [[tetration]] to base $b\!=\!2$ ==[[C++]] Generator of map]==
    (5,130 × 1,760 (1.53 MB)) - 11:59, 21 July 2020
  • File:Ack4bFragment.jpg
    Fragment of image [[Complex map]] of [[tetration]] to base $b\!=\!2$
    (3,457 × 1,776 (1.62 MB)) - 08:28, 1 December 2018
  • File:Ack4c.jpg
    [[Complex map]] of [[tetration to Sheldon base]] $b\!=\! Another version of this image is loaded as http://mizugadro.mydns.jp/t/index.php/File:Tetshel
    (5,130 × 1,760 (1.92 MB)) - 08:28, 1 December 2018
  • File:Ackerplot.jpg
    [[Explicit plot]] of the 5 [[Ackermann function]]s to base $\mathrm e$ ==General properties of [[Ackermann function]]s==
    (2,800 × 4,477 (726 KB)) - 08:28, 1 December 2018
  • File:Ackerplot400.jpg
    [[Explicit plot]] of the 5 [[Ackermann function]]s to base $\mathrm e$ ==General properties of [[Ackermann function]]s==
    (3,355 × 4,477 (805 KB)) - 08:29, 1 December 2018
  • File:Analuxp01t400.jpg
    Comparison of various fits of the [[natural titration]] with the [[complex map]s Lines of constant [[logamplitude]] $u$ and phase $v$ are shown in the complex plane:
    (2,083 × 3,011 (1.67 MB)) - 08:29, 1 December 2018
  • File:Analuxp01u400.jpg
    [[Complex map]]s of various approximations $f$ of [[natural tetration]]. ==Description of curves==
    (2,083 × 3,011 (1.72 MB)) - 08:29, 1 December 2018
  • File:Analuxp02t900.jpg
    Map of function is [[fixed point]] of natural [[logarithm]], $\ln(L)\!=\!L\!=\!\exp(L)$.
    (3,362 × 1,295 (987 KB)) - 08:29, 1 December 2018
  • File:E1e14z600.jpg
    Iterates of exponent to various bases $b$. ==[[C++]] generator of map for $b\!=\!\mathrm e$==
    (3,566 × 6,300 (1.85 MB)) - 08:34, 1 December 2018
  • File:E1eAuMap600.jpg
    [[Complex map]]s of the [[abel function]] of the [[exponent]] to the [[Henryk base]] and for inverse of the growing superexponent, id est,
    (3,543 × 5,338 (1.57 MB)) - 08:34, 1 December 2018
  • File:E1eghalfm3.jpg
    [[Complex map]] of upper half iterate of exponential to base $\eta=\exp(1/\mathrm e)$ ...n of the Two Regular Super-Exponentials to base exp(1/e). [[Mathematics of Computation]], v.81 (2012), p. 2207-2227.
    (1,750 × 1,341 (1.24 MB)) - 08:34, 1 December 2018
  • File:E1eiterT.jpg
    [[Iterate]] of exponential to the [[Henryk base]] $\eta=\exp(1/\mathrm e)$; id ess, the iterates of the [[transfer function]] $T(z)=\exp(z/\mathrm e)$.
    (2,166 × 2,179 (1.03 MB)) - 08:34, 1 December 2018
  • File:E1eplot8.png
    Explicit plot of the two superexponentials to base $\eta=\exp(1/\mathrm e)$ Superexponential to base $b$ is solution $F$ of the [[transfer equation]]
    (2,577 × 1,355 (226 KB)) - 08:34, 1 December 2018
  • File:E1esuma8.jpg
    [[Complex map]] of the growing [[superfunction]] of exponential to [[base e1e]] ...ryk base]]; and $F=\mathrm{SuExp}_{\eta,3}$ is real–holomorphic solution of the [[transfer equation]]
    (4,472 × 3,320 (1.76 MB)) - 08:34, 1 December 2018
  • File:E1eSuMap600.jpg
    [[Complex map]]s of two superexponentials to the [[Henryk base]] ==[[C++]] generator of upper map==
    (3,377 × 5,055 (1.37 MB)) - 08:34, 1 December 2018
  • File:E1etetma8.jpg
    [[Complex map]] of [[tetration]] to [[base e1e]] [[Tetration]] $F=\mathrm{tet}_{\eta}$ is real-holomorphic solution of equation
    (4,472 × 3,320 (1.69 MB)) - 08:34, 1 December 2018
  • File:Exp1exp2t.jpg
    Iterate of exponent (thin black lines) compared to the linar combination of $\exp$ and $\exp^2$, deawn with thick green lines. Iterates of exponent are evaluated through tetration tet and arctetration ate:
    (1,278 × 875 (296 KB)) - 08:35, 1 December 2018
  • File:Penplot.jpg
    [[Explicit plot]] of natural [[pentation]], ...ymptotic level $L\approx -1.8503545290271812$ is smallest real fixed point of [[natural tetration]].
    (1,266 × 2,100 (240 KB)) - 08:46, 1 December 2018
  • File:Sqrt27t.jpg
    [[Explicit plot]] of [[tetration]] to base $\sqrt{2}$ Usage: this is figure 16.1 of the book [[Суперфункции]] (2014, In Russian) <ref>
    (3,401 × 3,401 (475 KB)) - 08:52, 1 December 2018
  • File:Sqrt27u.png
    Check of the approximate symmetry of the [[explicit plot]] of [[tetration]] to base $\sqrt{2}$ in figure http://mizugadro.mydns.jp/t/inde Usage: this is figure 16.6 of the book [[Суперфункции]] (2014, In Russian) <ref>
    (856 × 507 (50 KB)) - 08:52, 1 December 2018
  • File:Sqrt2atemap.jpg
    [[Complex map]] of [[arctetration]] to base $\sqrt{2}$: Usage: this is figure 16.3 of the book [[Суперфункции]] (2014, In Russian) <ref>
    (1,758 × 1,741 (723 KB)) - 08:52, 1 December 2018
  • File:Sqrt2diimap80.jpg
    [[Complex map]] of iterate number i of exponent to base $\sqrt{2}$ constructed at its lower ("down") fixed point 2 Usage: this is figure 16.11 of the book [[Суперфункции]] (2014, In Russian) <ref>
    (2,302 × 2,306 (1.27 MB)) - 08:52, 1 December 2018
  • File:Sqrt2eitet.jpg
    [[iterate]]s of the [[esponent]] to base $\sqrt{2}$, Usage: this is figure 16.7 of the book [[Суперфункции]] (2014, In Russian) <ref>
    (3,051 × 3,022 (1.36 MB)) - 08:52, 1 December 2018
  • File:Sqrt2q2map600.jpg
    [[Complex map]] of the half iterate of exponent to base $\sqrt{2}$ regular at its lowest fixed point. Usage: this is figure 16.8 of the book [[Суперфункции]] (2014, In Russian) <ref>
    (1,766 × 1,750 (1.43 MB)) - 08:52, 1 December 2018
  • File:Sqrt2srav.png
    Comparison or two half iterate of exponent to base \( \sqrt{2} \) constructed at fixed point 2 and at fixed p Usage: this is figure 16.9 of the book [[Суперфункции]] (2014, In Russian) <ref>
    (2,532 × 1,639 (263 KB)) - 10:53, 24 June 2020
  • File:Sqrt2sufuplot.png
    They are real-holomorphic solutions \(F\) of the transfer equation ...ait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.
    (3,520 × 2,507 (408 KB)) - 10:11, 10 June 2022
  • File:Sqrt2tetatemap.jpg
    Range of validity of relation These lines provide the shading of the central part of the picture.
    (1,758 × 1,741 (1,008 KB)) - 08:52, 1 December 2018
  • File:Sqrt2tetmap.jpg
    [[Complex map]] of [[tetration]] to base $\sqrt{2}$: Usage: this is figure 16.2 of the book [[Суперфункции]] (2014, In Russian) <ref>
    (1,758 × 1,741 (656 KB)) - 08:52, 1 December 2018
  • File:Sqrt2uiimap80.jpg
    [[Complex map]] of iterate number i of exponent to base $\sqrt{2}$ constructed at its upper fixed point 4: Usage: this is figure 16.12 of the book [[Суперфункции]] (2014, In Russian) <ref>
    (2,302 × 2,306 (1.84 MB)) - 08:52, 1 December 2018
  • File:Tetma.jpg
    [[Complex map]] of the [[natural tetration]] without labels. The low resolution draft also had been loaded at the site of ingrampublishing
    (3,341 × 1,675 (1.89 MB)) - 08:53, 1 December 2018
  • File:Vladi08.jpg
    Agreement of approximations of tetration by elementary functions with the original representation through ...to the similar representation through the Cauchi integral, but the contour of integration is displaced for 1/2 to the left.
    (787 × 375 (117 KB)) - 08:56, 1 December 2018
  • Ackermann function
    ...at used in the [[Computability theory]]. While no commonly accepted system of notations is established, at the reference to the Ackermann function, eithe ...ontent of this article is published in 2014 at [[Applied and Computational Mathematics]]
    10 KB (1,534 words) - 06:44, 20 July 2020
  • Analuxpf3c.cin
    ..., that provides approximation of [[natural tetration]] for moderate values of the argument. // This fit had been used to guess the asymptotic behaviour of [[tetration]] at \(\mathrm i \infty\).
    1 KB (253 words) - 18:48, 30 July 2019
  • Applied and Computational Mathematics
    [[Applied and Computational Mathematics]] is [[scientific journal]] dedicated to development of mathematical principles and practical issues in computational mathematics.
    1 KB (134 words) - 06:58, 1 December 2018
  • Base e1e
    [[File:Expe1emapT1000.jpg|200px|thumb|[[Complex map|Map]] of \(~f\!=\!\eta\!=\!\exp_{\exp(1/\mathrm e)}~\); here \(~u+\mathrm i v=f(x\!+ [[File:Loge1emapT1000.jpg|200px|thumb|[[Complex map|Map]] of \(~f\!=\!\log_{\exp(1/\mathrm e)}~\); here \(~u+\mathrm i v=f(x\!+\!\mathrm
    4 KB (559 words) - 17:10, 10 August 2020
  • Conjecture on superfunctions
    http://en.wikipedia.org/wiki/File:Boy_on_snow_sled,_1945.jpg Father of JGKlein. Boy on snow sled, 1945. ...n of sin is expressed with sinˆn(z)=SuSin(n+AuSin(z)), where the number n of iteration has no need to be integer. ..
    7 KB (1,031 words) - 03:16, 12 May 2021
  • Exotic iteration
    ...[Regular iteration]] is not possible: in the leading term of the expansion of superfunction with exponentials, the increment \(k\!=\!\ln(T'(L)\) becomes However, even if the \(T'(L)\!=\!1\), construction of superfunction is possible. Few examples are considered in this article.
    11 KB (1,715 words) - 18:44, 30 July 2019
  • Mathematics of Computation
    [[Mathematics of Computation]] ([[MOC]]) is [[Scientific journal]] dedicated to numerical analysis, computational discrete mathematics, number theory, algebra, combinatorics, and related fields.
    2 KB (344 words) - 07:02, 1 December 2018

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