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• Regular Iteration
  ...fixpoint $a$ is called regular, iff $\phi$ is analytic at $a$ or has an [[asymptotic powerseries development]] at $a$. The asymptotic expansion can be obtained also for the [[Abel function]] $~G=F^{-1}~$, eith
  20 KB (3,010 words) - 18:11, 11 June 2022
• Mathematica
  ...orial]], [[Abel Factorial]], etc.; of order of a dozen coefficients of the asymptotic expansion can be calculated analytically in the [[real time]]. (If manually As any other software, Mathematica has bugs. One of them is related to the asymptotic expansion of the [[Bessel function]] of non-trivial argument.
  12 KB (1,901 words) - 18:43, 30 July 2019
• Yulya function
  Asymptotic expansion at small values of the argument has the form The expansions (7),(8),(9) above can be inverted, giving the asymptotical representation f
  12 KB (1,754 words) - 18:25, 30 July 2019
• Tania function
  The expansions of Tania in diffrent cases, and, in particular, at the [[branchpoint]]s \(z For the evaluation, the asymptotic can be written also as follows:
  27 KB (4,071 words) - 18:29, 16 July 2020
• Coshc
  ==Asymptotic expansions==
  4 KB (509 words) - 18:26, 30 July 2019
• ArcCosc
  In the figure with the [[explicit plot]] of acosc, it is compared with its asymptotic denoted with name \(\mathrm{Left}_3\). ==More expansions of ArcCosc==
  8 KB (1,137 words) - 18:27, 30 July 2019
• Acosc1
  ...|thumb| Acosc1(\(x\)) versus \(x\), red; [[ArcCosc]](\(x\)), blue and some asymptotic]] ...hm; however, the accurate handling of the branches is required to use this asymptotic for the evaluation.
  6 KB (896 words) - 18:26, 30 July 2019
• BesselJ0
  Coefficients of the expansions above can be calculated and verified with the [[Mathematica]] code below: The asymptotic expansions for [[BesselJ0]] diverge, but are useful for precise evaluation of [[Besseo
  6 KB (913 words) - 18:25, 30 July 2019
• BesselK0
  that has asymptotic ==Expansions==
  3 KB (394 words) - 18:26, 30 July 2019
• BesselJ1
  ==Expansions== ...complex(double) arithmetics is available. For large values of \(|z|\), the asymptotic expansion can be used for the precise evaluation:
  3 KB (439 words) - 18:26, 30 July 2019
• Bessel function
  with the following asymptotic behaviour: </ref> suggest the following expansions (See 8.4.5.5)
  13 KB (1,592 words) - 18:25, 30 July 2019
• BesselH0
  ==Asymptotic expansions== Some expansions of square of [[BesselH0]] look counter-intuitive and require analysis.
  4 KB (509 words) - 18:26, 30 July 2019
• Zooming equation
  ==Asymptotic expansion== ...ot known, these \(f\) and \(g\) can be constructed thrush their asymptotic expansions at small values of the argument. Assuming that \(T\) is regular at zero, ex
  10 KB (1,627 words) - 18:26, 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
• ArcTra
  However the independent implementation of ArcTra can be arranged using its asymptotic properties. ==Expansions at infinity, logarithmic growth==
  10 KB (1,442 words) - 18:47, 30 July 2019
• 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
• Amplitude of oscillator function
  ...ymptotic expansions of various functions with the oscillator function, the asymptotic behaviour of ...ymptotic approximation are shown in figure at right, together with two its asymptotic approximations.
  6 KB (770 words) - 18:44, 30 July 2019
• Bohr radius
  ...\(c\) are used to denote coefficients of some polynomial and/or asymptotic expansions.
  2 KB (228 words) - 18:46, 30 July 2019
• Exotic iteration
  For some fixed natural number \(M>0\), the asymptotic expansion of the superfunction \(f\) can be constructed as follows: providing asymptotic agreement with the transfer equation (1).
  11 KB (1,715 words) - 18:44, 30 July 2019
• Kori
  [[File:Koriasmap.jpg|200px|thumb|Complex map of the asymptotic approximation [[korias]] with \(m\!=\!11\); For large values of the argument, the asymptotic expansion of kori can be written in terms of amplitude and phase, in analog
  14 KB (1,943 words) - 18:48, 30 July 2019

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