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- ...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]] $~G=F^{-1}~$, eith20 KB (3,010 words) - 18:11, 11 June 2022
- ...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
- Asymptotic expansion at small values of the argument has the form The expansions (7),(8),(9) above can be inverted, giving the asymptotical representation f12 KB (1,754 words) - 18:25, 30 July 2019
- 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
- ==Asymptotic expansions==4 KB (509 words) - 18:26, 30 July 2019
- 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
- ...|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
- 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 [[Besseo6 KB (913 words) - 18:25, 30 July 2019
- that has asymptotic ==Expansions==3 KB (394 words) - 18:26, 30 July 2019
- ==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
- 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
- ==Asymptotic expansions== Some expansions of square of [[BesselH0]] look counter-intuitive and require analysis.4 KB (509 words) - 18:26, 30 July 2019
- ==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, ex10 KB (1,627 words) - 18:26, 30 July 2019
- D.Kouznetsov. Entire Function with Logarithmic Asymptotic. ...(z)|>\varepsilon\), \( |z| \rightarrow \infty\), [[SuTra]] has logarithmic asymptotic behavior9 KB (1,285 words) - 18:25, 30 July 2019
- 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
File:TaniaBigMap.png [[Category:Asymptotic expansions]](851 × 841 (654 KB)) - 08:53, 1 December 2018File:Arcnembrat.jpg For very small or very large values of $|z|$, the asymptotic expansions can be used.(2,878 × 2,822 (1.92 MB)) - 08:30, 1 December 2018- ...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
- ...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
- ...\(c\) are used to denote coefficients of some polynomial and/or asymptotic expansions.2 KB (228 words) - 18:46, 30 July 2019