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• Regular iterate
  ...sion of the [[Abel function]] \(G\) in vicinity of \(L\) and corresponding expansion of the [[superfunction]] \(F=G^{-1}\), ...ument of the [[superfunction]] to the range of values where the asymptotic expansion provides the required precision.
  1 KB (178 words) - 06:42, 20 July 2020
• Korias
  [[korias]] is asymptotic approximation of function [[kori]]. At large values of the argument, \(|z|\gg 1\), the asymptotic approximation appears as [[korias]] defined with
  2 KB (328 words) - 10:27, 20 July 2020
• Theorem on increment of tetration
  [[Theorem on increment of tetration]] is statement about asymptotic behavior of solution of the [[Transfer equation]] with exponential transfer ...ry part of the growing factor \(K\) and that of the increment \(k\) of the asymptotic solution versus logarithm of the base.
  4 KB (548 words) - 14:27, 12 August 2020
• Coshc
  ==Asymptotic expansions== This series can be inverted giving the expansion for the inverse function [[ArcCoshc]]:
  4 KB (509 words) - 18:26, 30 July 2019
• SuNem
  Also, the specific asymptotic behaviour at infinity is assumed, ==Asymptotic expansion==
  6 KB (968 words) - 11:18, 23 December 2025
• Amos
  ...cplot.jpg|256px|thumb|\(y\!=\!\mathrm{Amos}(x)\), black curve, and two its asymptotic approximaitons]] For comparison, the two its asymptotic approximations are also plotted with coloured curves.
  6 KB (883 words) - 18:44, 30 July 2019
• Morias.cin
  // [[Morias.cin]] is complex double implementation in [[C++]] of the asymptotic approximation [[morias]] of the [[Morinaga function]] for large values of t // [[Category:Asymptotic expansion]] [[Category:Bessel function]] [[Category:C++]] [[Category:Morinaga functio
  2 KB (188 words) - 07:03, 1 December 2018
• ArcFactorial
  ...acplotT2px300.png|600px|right|thumb|\(y=\mathrm{ArcFactorial}(x)\) and its asymptotic approximation]] ==Expansion at Homer==
  3 KB (376 words) - 18:26, 30 July 2019
• Arcfactorial
  ...acplotT2px300.png|600px|right|thumb|\(y=\mathrm{ArcFactorial}(x)\) and its asymptotic approximation]] ==Expansion at Homer==
  3 KB (414 words) - 18:26, 30 July 2019
• Exotic iteration
  ...ase, the [[Regular iteration]] is not possible: in the leading term of the expansion of superfunction with exponentials, the increment \(k\!=\!\ln(T'(L)\) becom ...ents, that may (and should) depend on the coefficients \(b\), \(c\), .. of expansion of the transfer function \(T\) at zero.
  11 KB (1,715 words) - 18:44, 30 July 2019
• AuTra
  ==Asymptotic expansion== The asymptotic expansion for AuTra for large negative values of the argument can be obtained, invert
  6 KB (1,009 words) - 18:48, 30 July 2019
• SuZex
  The first two terms of the asymptotic expansion of [[SuZex]] can be used as the definition. ==Asymptotic expansion==
  7 KB (1,076 words) - 18:25, 30 July 2019
• Morias
  [[morias]] is asymptotic approximation of function [[mori]] at large values of its argument. The coefficients \(f\) and \(g\) can be calculated from the asymptotic expansion of the [[Hankel function]];
  3 KB (456 words) - 18:44, 30 July 2019
• Bessel function
  with the following asymptotic behaviour: Peerhaps, these expressions can be used to deduce the expansion suitable for the numerical implementation.
  13 KB (1,592 words) - 18:25, 30 July 2019
• SuTra
  D.Kouznetsov. Entire Function with Logarithmic Asymptotic. ...(z)|>\varepsilon\), \( |z| \rightarrow \infty\), [[SuTra]] has logarithmic asymptotic behavior
  9 KB (1,285 words) - 18:25, 30 July 2019
• Zooming equation
  ==Asymptotic expansion== ...\(g\) are not known, these \(f\) and \(g\) can be constructed thrush their asymptotic expansions at small values of the argument. Assuming that \(T\) is regular
  10 KB (1,627 words) - 18:26, 30 July 2019
• AuSin
  ==Expansion at \(\pi/2\)== Expansion at \(\pi/2\) has the following form:
  6 KB (927 words) - 07:13, 17 October 2025
• SuZex approximation
  ==Taylor expansion at zero== [[File:SuZexoMapJPG.jpg|600px|thumb|Fig.4. Map od the Asymptotic approximation \(Q_{20}~\) by equation (\(~\)); \(~u\!+\!\mathrm i v= Q_{20
  14 KB (2,037 words) - 18:25, 30 July 2019
• BesselJ1
  ...ble) arithmetics is available. For large values of \(|z|\), the asymptotic expansion can be used for the precise evaluation: This asymptoric expansion is used for the numerical implenentation. However, \(z\) should not approac
  3 KB (439 words) - 18:26, 30 July 2019
• Kneser expansion
  [[Kneser expansion]] is asymptotic representation of superexponential constructed at its fixed point. [[Category:Kneser expansion]]
  2 KB (325 words) - 22:50, 15 August 2020

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