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• 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
• AuZex
  ...along the real axis. For this reason, namely this fixed point is chosen as asymptotic value of [[SuZex]] at minus infinity. Correspondently, its inverse function ...expansion of the [[Abel function]]. For the transfer function [[zex]], the expansion of the Abel function begins with minus first power and logarithmic terms:
  6 KB (899 words) - 18:44, 30 July 2019
• Power function
  and the asymptotic analysis. For \(a_1\!=\!1\), these coefficients can be calculated with the This code confirms, that the primary expansion is just truncated series go expansion of exponent in the exact [[superfunction]] [[SuPow]]
  15 KB (2,495 words) - 18:43, 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
• 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
• 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. ==Expansion at unity==
  10 KB (1,442 words) - 18:47, 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

• File:Besselh0mapT100.png For large values, the direct asymptotic expansion should be used instead. (2,284 × 1,164 (1.65 MB)) - 08:31, 1 December 2018

• File:DSC01695bangkok.JPG .. Here is primary approximation with two terms held in the asymptotic expansion .. (2,048 × 1,536 (1.13 MB)) - 09:43, 21 June 2013

• File:SimudoyaTb.png ...ry approximation of $F$ with one term and with two terms of the asymptotic expansion, respectively. (3,388 × 1,744 (537 KB)) - 08:51, 1 December 2018

• File:SuZex0map48small.png [[Complex map]] of the truncated [[Taylor expansion]] of function [[SuZex]] at zero; polynomial $P_{48}$ is plotted, $u\!+\!\ma Coefficients $c$ are calculated with [[Mathematica]], from the [[asymptotic expansion]] at large $-z$, condition $~\mathrm{SuZex}(0)\!=\!1~$ and the [[transfer e (1,230 × 1,230 (734 KB)) - 09:43, 21 June 2013

• File:SuZexD1mapT.png [[SuZex]] is built-up at the fixed point zero from asymptotic behavior; the approximation below is implemented: ...get the camera-ready copy. For the precise computation, more terms in the expansion (1) should be calculated. (2,576 × 2,559 (1.04 MB)) - 08:53, 1 December 2018

• File:SuZexo20testTjpg.jpg [[Agreement map]] for the asymptotic approximation $Q_{20}$ of function [[SuZex]]. ...bs(z) < 1.6 ) return SuZexTay0(z) ; // I made the Taylor expansion for this case (4,576 × 4,542 (1.81 MB)) - 17:14, 25 September 2013

• File:SuZexoMapJPG.jpg [[Complex map]] of the asymptotic expansion $Q_{20}$ of function [[SuZex]]; $~u\!+\!\mathrm i v\!=Q_{20}\!(x\!+\!\mathr and the expansion by orders of $1/z$. Here [[zex]](z)$\,=z\,\exp(z)~$.<br> (4,576 × 4,542 (1.73 MB)) - 17:15, 25 September 2013

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  File:SuZexoMapT.png [[Complex map]] of the asymptotic expansion $Q_{20}$ of function [[SuZex]]; $u\!+\!\mathrm i v\!=Q_{20}(x\!+\!\mathrm i (4,576 × 4,542 (1.57 MB)) - 09:43, 21 June 2013

• File:TaniaBigMap.png The [[complex map]] of the truncated expansion of the [[Tania function]] at large values of its argument. Function <br> [[Category:Asymptotic expansions]] (851 × 841 (654 KB)) - 08:53, 1 December 2018

• File:TaniaNegMapT.png [[Complex map]] of the truncation of the asymptotic expansion of the [[Tania function]] [[Category:Asymptotic series]] (1,773 × 1,752 (306 KB)) - 09:39, 21 June 2013

• File:Tetreal2215.jpg // but for the serious numerial analysis the number of terms in the expansion should be increased;<br> // and for large values of the imaginary part, the asymptotic representaton should be used instead. (876 × 881 (130 KB)) - 09:38, 21 June 2013

• Nori
  ==Expansion at zero== if evaluated with complex double variables, the first 24 terms of this expansion provide of order of 15 correct decimal digits for \(|z|<8\).
  13 KB (1,759 words) - 18:45, 30 July 2019

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