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• Tetration
  Natural [[tetration]] (dashed) and other [[Ackermann function|ackermanns]] [[Tetration]] (or Tetrational) \({\rm tet}_b\) to base \(b \in \mathbb R\), \(b\!>1\)<br>
  21 KB (3,175 words) - 23:37, 2 May 2021
• Mapping
  '''Mapping''' means function from some space to itself or to another space, and also the graphical representation of such a function. Su ...pography]], the 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
  ...nction considered was super-exponential or [[tetration]], that corresponds to In particular, the [[Ackernann functions]] and [[tetration]] can be interpreted in terms of [[superfunction]]s.
  25 KB (3,622 words) - 08:35, 3 May 2021
• Natural pentation
  [[Natural pentation]] is [[pentation]] to base \(\mathrm e\!=\!\exp(1)\!\approx\!2.71\); it is [[holomorpic function]] in the range that includes the real axis.
  7 KB (1,090 words) - 18:49, 30 July 2019
• Square root of factorial
  ...lomorphic function]] al least in some vicinity of [[halfline]] along the [[real axis]], \(h\circ h=\mathrm{Factorial}\). It is assumed that \(z\!=\!2\) is \(\sqrt{!\,}(2)=2\). Along the real axis, the square root of factorial grows faster than any [[polynomial]], bu
  13 KB (1,766 words) - 18:43, 30 July 2019
• Regular Iteration
  '''Regular Iteration''' or '''regular iterate''' refer to the [[fractional iterate]] a holomorphic function that is holomorphic in vi ...d the fractional iterates, regular at different fixed points, have no need to coincide <ref name="sqrt2">
  20 KB (3,010 words) - 18:11, 11 June 2022
• SuperFactorial
  ...enter>Fig.1. \(y\!=\!x!\) and \(y\!=\! \mathrm{SuperFactorial}(x)\) versus real \(x\)</center></small> ...on of SuperFactorial causes the only diagnostic message and cannot be used to plot the SuperFactorial.</ref>
  18 KB (2,278 words) - 00:03, 29 February 2024
• Transfer function
  ...ansfer equation]], the [[Abel equation]]; the transfer function is assumed to be given function that appear in these equations. The solutions of these eq ...r a given transfer function, the additional restrictions should be applied to make the [[superfunction]] and the [[Abel function]] unique
  11 KB (1,644 words) - 06:33, 20 July 2020
• Logarithm
  For the natural exponential, id est, exponential to base [[e]], the logarithm is called "natural" ==Various values of base==
  4 KB (661 words) - 10:12, 20 July 2020
• ArcTetration
  [[ArcTetration]] \( \mathrm{ate} \) is inverse function of [[tetration]] For real values of the argument,
  7 KB (1,091 words) - 23:03, 30 November 2019
• Tania function
  ...[Tania function]] (thin curve) to the [[Shoka function]] (thick curve) for real values of the argument]] ...maginary axis and then along the straight line (parallel to the real axis) to the point \(z\).
  27 KB (4,071 words) - 18:29, 16 July 2020
• Doya function
  In vicinity of the real axis (While \(|\Im(z)| \!<\! \pi\)), the [[Doya function]] can be expressed ...for comparison of superfunctions \(F\) for various cases, it is convenient to keep relation \(F(0)=1\)
  19 KB (2,778 words) - 10:05, 1 May 2021
• Table of superfunctions
  is called [[superfunction]] with respect to \(T\). ...se function, id est, \(G=F^{-1}\) is called [[Abel function]] with respect to \(T\); it satisfies the [[Abel equation]]
  11 KB (1,565 words) - 18:26, 30 July 2019
• Square root of exponential
  Such a \(\varphi\) is assumed to be [[holomorphic function]] for some domain of values of \(z\). ...sto \exp(z)^{1/2}\); in the range of holomorphism, the last can be reduced to \(\exp(z/2)\).
  5 KB (750 words) - 18:25, 30 July 2019
• Iteration
  The zeroth iteration of any non-trivial function is supposed to be [[Identity function]]. Similar notations, where the superscript is used to indicate the number of iterate is used also in [[quantum mechanics]] and th
  14 KB (2,203 words) - 06:36, 20 July 2020
• Natural tetration
  [[Natural tetration]] is [[tetration]] to base \(\mathrm e=\exp(1)\approx 1.71~\). Natural tetration is denoted as \(\mathrm {tet}\) or \(\mathrm {tet}_{\mathrm e}\); it satis
  14 KB (1,972 words) - 02:22, 27 June 2020
• Filog
  ...function]] that expresses the [[fixed point]]s of [[logarithm]] to complex base. for base \(b\!=\!\exp(z)\).
  4 KB (572 words) - 20:10, 11 August 2020
• Tetration to Sheldon base
  ...g|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
• WrightOmega
  ...maginary axis and then along the straight line (parallel to the real axis) to the point \(z\). The contour of integration of equation (1) can be modified without to affect the values of the function, but it should not intersect the cut line
  4 KB (610 words) - 10:22, 20 July 2020
• ArcLambertW
  The number \(n\) of iteration hax no need to be integer. For several real values of \(n\), the \(n\)th iteration of [[zex]] by (8) is plotted in figu ...ar to the plots of iterates of other functions with fast growth along the real axis.
  3 KB (499 words) - 18:25, 30 July 2019

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