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- In partucular, the "new expansion" and the asymptotic analysis with small parameter \(|1/z|\) determines21 KB (3,175 words) - 23:37, 2 May 2021
- // 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.6 KB (1,030 words) - 18:48, 30 July 2019
- ...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
- ...fixpoint $a$ is called regular, iff $\phi$ is analytic at $a$ or has an [[asymptotic powerseries development]] at $a$. is searched in form of the expansion (2)20 KB (3,010 words) - 18:11, 11 June 2022
- where \(K=\exp(k)\). The expansion of the left hand side of equation (1) into the power series with respect to ...therefore get the required precision of evaluation of \(F\). <!--with the asymptotic series.!-->18 KB (2,278 words) - 00:03, 29 February 2024
- ...Abel Factorial]], etc.; of order of a dozen coefficients of the asymptotic expansion can be calculated analytically in the [[real time]]. (If manually, each suc ...r 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
- ===Expansion at small values of parameter=== Asymptotic expansion at small values of the argument has the form12 KB (1,754 words) - 18:25, 30 July 2019
- In order to simplify the expansion at the branchpoints (see below), the cut lines are directed to the left, pa ===Expansion of Tania at infinity===27 KB (4,071 words) - 18:29, 16 July 2020
- Expansion at small values of the argument can be written as follows: Expansion at large values of the argument can be written as follows:19 KB (2,778 words) - 10:05, 1 May 2021
- ==Asymptotic expansions== This series can be inverted giving the expansion for the inverse function [[ArcCoshc]]: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 \(\mathrm{Left}_3\). The subscript 3 indicates that the only 3 terms taken into account in the expansion. Function \(\mathrm{Left}_3(z)\) approximates \(\mathrm{acosc}(z)\) in the8 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
- ...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
- ==Asymptotic estimate of the guiding efficiency== The expansion of function [[acosq]] (which appears in equation (37)) at zero has to follo15 KB (2,070 words) - 18:47, 30 July 2019
- ==Expansion at zero== The straightforward Taylor expansion at zero can be written as follows:6 KB (913 words) - 18:25, 30 July 2019
- ...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 approac3 KB (439 words) - 18:26, 30 July 2019
- 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
- ...order to avoid the loss of precision, at small values of the argument the expansion can be used: ...[[regular iteration]], the [[superfunction]] \(F\) can be constructed with asymptotic behavior10 KB (1,479 words) - 05:27, 16 December 2019
- ==Asymptotic behavior== Many Taylor coefficients of the expansion can be calculated with some [[Mathematica]] or [[Maple software]]; the seri10 KB (1,507 words) - 18:25, 30 July 2019
- 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