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- ==The Taylor expansion== The [[Taylor expansion]] of <math>z!</math> at <math>z=0</math>, or the [[MacLaurin expa27 KB (3,925 words) - 18:26, 30 July 2019
- ...exp(1/{\rm e})\), \(z\!\approx 0\), then it is expandable into the Taylor series21 KB (3,175 words) - 23:37, 2 May 2021
- ...\(F(k\!+\!1)\) into the equation above, and the expansion to the [[Taylor series]] with respect to \(\varepsilon\) gives the equation for \(k\) and the chai5 KB (798 words) - 18:25, 30 July 2019
- At \(|z|\gg 1\), the truncated series (7) can be used for the evaluation of \(\mathrm{Tania}(z)\), while the argu ...on of the approximation is less than 3; outside that region, the truncated series with the last term of order of27 KB (4,071 words) - 18:29, 16 July 2020
- Each of the values above can be used to construct the simple Taylor expansion, suitable for the approximations. Although the ArcCos of real arg Inversion of the series gives the expansion for ArcCos at the branch point \(-1\):5 KB (754 words) - 18:47, 30 July 2019
- ...equal to distance between the branch points; so, in vicinity of zero both series converge exponentially, and, with more terms in the truncation, overlap pre ...straightforward calculation of a dozen of terms of such an expansion. The series converges at \(|z|<\mathrm{Tarao}_1 \approx 0.161228034325064\)6 KB (896 words) - 18:26, 30 July 2019
- The straightforward Taylor expansion at zero can be written as follows: The series converges in the whole complex plane and, at the complex(double) arithmetic6 KB (913 words) - 18:25, 30 July 2019
- The [[Shoko function]] has series of branchpoints at \(r+\pi(1\!+\!2 n) \mathrm i\) for integer values of \(n and the series of cutlines \(r+\pi(1\!+\!2 n)\mathrm i + t\) for integer values of \(n\)10 KB (1,507 words) - 18:25, 30 July 2019
- ==Taylor expansion at zero== Fig.3. [[Taylor approximation]] (4) with 48 terms; \(!u\!+\!\mathrm i v= P_{48}(x\!+\!\math14 KB (2,037 words) - 18:25, 30 July 2019
- As nori is entire function, it can be expanded to convergent Taylor series in any point. In particular, the expansion at its first zero appears as ...ic integration with exponential; so, the representation with the truncated series above can be useful for the evaluation of the [[Fourier integral]]s with fu13 KB (1,759 words) - 18:45, 30 July 2019
- As kori is entire function, the Taylor series absolutely converge at any value of the argument. ...ay have sense to cut the series at 6th or at 7th term; then, the truncated series provide good estimate of \(\mathrm{kori}(z)\) for \(|z|>30\). In vicinity o14 KB (1,943 words) - 18:48, 30 July 2019
- http://news.usni.org/2014/04/23/uss-taylor-returns-black-sea-3-nato-ships-now-region Sam LaGrone. USS Taylor Returns to Black Sea, 3 NATO Ships Now in Region. Published: April 23, 2014104 KB (12,626 words) - 23:29, 17 December 2019
- Ukraine’s parliament on Tuesday approved a series of joint military exercises with NATO countries that would put U.S. troops Warship USS Donald Cook leaves Black Sea. World April 25, 16:25. USS Taylor previously remained in the sea from February 5 to March 9, eleven days long342 KB (13,538 words) - 18:47, 30 July 2019
- ...] is approximation of natural [[tetration]], implemented in [[C++]] as the Taylor expansion at zero with 50 terms. //[[Category:Tetration]] [[Category:Book]] [[Category:C++]] [[Category:Taylor series]]2 KB (101 words) - 14:55, 12 July 2020
- Ukraine’s parliament on Tuesday approved a series of joint military exercises with NATO countries that would put U.S. troops Warship USS Donald Cook leaves Black Sea. World April 25, 16:25. USS Taylor previously remained in the sea from February 5 to March 9, eleven days long343 KB (13,572 words) - 18:48, 30 July 2019
