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• Factorial
  ...teration can be calculated also for non-integer values of \(n\), number of iterations can be complex <ref name="qf">
  27 KB (3,925 words) - 18:26, 30 July 2019
• Tetration
  For small values of \(z\), the iterations of formula \(F(z)=\ln(F(z\!+\!1))\!~ \mathrm e\) In this expression, the number \(c\) of iterations ahs no need to be [[integer number|integer]]; however, at integer values,
  21 KB (3,175 words) - 23:37, 2 May 2021
• Superfunction
  ...f superfunctions came from the application to the evaluation of fractional iterations of functions. The third (and last) argument indicates the number of iterations.
  25 KB (3,622 words) - 08:35, 3 May 2021
• Square root of factorial
  ...me of iterated function, and the last argument is interpreted as number of iterations ...necessary integer) iterations of functions and algebraic analysis of such iterations.
  13 KB (1,766 words) - 18:43, 30 July 2019
• Regular Iteration
  same periods. In general, the [[SuperFunction]]s constructed with regular iterations at different fixed points are not equivalent <ref name="karlin"> ...umb|primary approximations by (18) and (19), brown and red curves, and the iterations of $T$ by (17) for $n=1,2,3,4$. The exact superfunction $F$ by (20) is show
  20 KB (3,010 words) - 18:11, 11 June 2022
• SuperFactorial
  ...belFactorial and the SuperFactorial allow to express (and to evaluate) the iterations of Factorial in the following way: where number \(c\) of iterations has no need to be integer; it can be even complex, and for some domain of \
  18 KB (2,278 words) - 00:03, 29 February 2024
• Tetration Forum
  ...tration]] and related topics about [[superfunction]]s and various kinds of iterations. The logo is shown at the figure at right.
  652 bytes (87 words) - 14:27, 20 June 2013
• Transfer equation
  ...from some domain in the set of complex numbers, where the number \(c\) of iterations have no need to be integer;
  3 KB (519 words) - 18:27, 30 July 2019
• Abel equation
  ...meters \(c\) and \(d\) have no need to be integer. For the case of integer iterations, \(T^{-1}\) is inverse function of \(T~, ~ ~\) [[Category:Iterations]]
  4 KB (598 words) - 18:26, 30 July 2019
• Nest
  ...est''' is name of function in the [[Mathematica]] software, that evaluates iterations of a function. ...d function, \(z\) is initial value of the argument, and \(c\) is number of iterations.
  3 KB (438 words) - 18:25, 30 July 2019
• Mathematica
  ...r 2011), the only natural constants are allowed as values of the number of iterations. Fore some function \(f\), the \(f^c\) is allowed only for an integer value
  12 KB (1,901 words) - 18:43, 30 July 2019
• Yulya function
  ===Iterations=== Using the initial approximation (35), very few iterations are sufficient to get several correct digits in the resulting implementatio
  12 KB (1,754 words) - 18:25, 30 July 2019
• LambertW function
  ...[[TORI]], the upper superscript after the function indicates the number of iterations, and the upper superscript after the argument and the closing parenthesis i
  8 KB (1,107 words) - 18:26, 30 July 2019
• Fourier transform
  The iterations of the Fourier operator ho not provide a wide variety, because
  11 KB (1,501 words) - 18:44, 30 July 2019
• Table of superfunctions
  11 KB (1,565 words) - 18:26, 30 July 2019
• Square root of exponential
  5 KB (750 words) - 18:25, 30 July 2019
• Iteration
  The second argument is initial value of the iterations, and the last argument is number of iteration. ...2012, the [[Nest]] is implemented only for the cases, when number \(n\) of iterations can be simplified to a [[natural number]], expressed with integer constant.
  14 KB (2,203 words) - 06:36, 20 July 2020
• Natural tetration
  The number \(c\) of iterations has no need to be integer; in particular, it can be a fration, an irrationa The non–integer iterations of exponential give the class of functions that grow faster than any polyno
  14 KB (1,972 words) - 02:22, 27 June 2020
• Iterated integral
  ...nested integration and the differentiation for the non–integer number of iterations. ==Negative number of iterations==
  9 KB (1,321 words) - 18:26, 30 July 2019
• Iterated Cauchi
  ...ten significant digits of the solution can be achieved within few tens of iterations. [[File:TetSheldonImaT.png|500px|right|thumb|First iterations for the [[Tetration to Sheldon base]]; \(f=f(x)\) versus \(x\) ]]
  6 KB (987 words) - 10:20, 20 July 2020
• ArcCosc
  ...e inverse function. Then, the Newtom method converges quickly: from 4 to 7 iterations are applied giving at least 14 correct decimal digits in the result.
  8 KB (1,137 words) - 18:27, 30 July 2019
• ArcSinc
  ...he leading terms of the expansions above as the initial approach; then few iterations of the [[newton method]] five of order of 15 correct significant figures.
  4 KB (563 words) - 18:27, 30 July 2019
• Logistic operator
  following the general rule of construction of iterations of a transfer function with specified [[Superfunction]] and [[Abel function ...e evaluation are supplied. With these functions, the explicit plot of some iterations of the logistic operators are
  6 KB (817 words) - 19:54, 5 August 2020
• ArcKeller
  ...ion]]s in terms of the elementary functions. Expressions, analogous to the iterations of the [[Keller function]], appeared in publications by U.Keller
  4 KB (545 words) - 18:26, 30 July 2019
• ArcLambertW
  ==Iterations of zex== ...ex]], called [[SuZex]], and the [[Abel function]], called [[AuZex]], the [[iterations]] of [[zex]] can be expressed as follows:
  3 KB (499 words) - 18:25, 30 July 2019
• SuZex approximation
  ...ould have sense to get more terms in asymptotic expansion (9) and use more iterations of function [[zex]] in (14). However, the 15 digits seem to be more than su
  14 KB (2,037 words) - 18:25, 30 July 2019
• AuZex
  Iterations of equation (3) gives the relations
  6 KB (899 words) - 18:44, 30 July 2019
• Mandelbrot polynomial
  In this expression, number \(n\) of iterations has no need to be integer; the [[Mandelbrot polynomial]] can be iterated ar
  2 KB (229 words) - 18:44, 30 July 2019
• Iterate of exponential
  ...defines the \(n\)th iterate of exponential for any complex number \(n\) of iterations. In addition, for negative number \(n\) of iterations (and, in particular, for \(n=-1\)), there is cut line along the negative pa
  7 KB (1,161 words) - 18:43, 30 July 2019
• Iterate of linear fraction
  the halfiteration and the complex iterations are straightforward. ...ot yet allow to use it for non-integer number of iterate; if the number of iterations cannot be expressed with some positive integer constant, Mathematica genera
  13 KB (2,088 words) - 06:43, 20 July 2020
• AuSin
  ==Iterations or sin== WIth SuSin and AuSin, Iterations of sin can be presented in the following way:
  5 KB (761 words) - 18:48, 30 July 2019
• Sin
  ==Representation through [[SuSin]] and [[AuSin]] and iterations==
  4 KB (680 words) - 18:43, 30 July 2019
• SuSin
  ...TORI]], the superscript after a name of a function indicates the number of iterations. This notation is borrowed from [[Quantum mechanics]], where Iterations of function sin, beginning with unity, indicate the set of specific values:
  15 KB (2,314 words) - 18:48, 30 July 2019