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• Factorial
  The Tailor expansion of <math>z!</math> at the point <math>z=\nu_0</math> can be writen ax follo The coefficients of this expansion are copypasted in the table below:
  27 KB (3,925 words) - 18:26, 30 July 2019
• Tetration
  In partucular, the "new expansion" ...ox \! \exp(1/{\rm e})\), \(z\!\approx 0\), then it is expandable into the Taylor series
  21 KB (3,175 words) - 23:37, 2 May 2021
• Holomorphic extension of the Collatz subsequence
  ...)\) and \(F(k\!+\!1)\) into the equation above, and the expansion to the [[Taylor series]] with respect to \(\varepsilon\) gives the equation for \(k\) and t
  5 KB (798 words) - 18:25, 30 July 2019
• Tania function
  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
• ArcCos
  Each of the values above can be used to construct the simple Taylor expansion, suitable for the approximations. Although the ArcCos of real argument is i ===Expansion of ArcCos at the branch point===
  5 KB (754 words) - 18:47, 30 July 2019
• Acosc1
  ...n the truncation, overlap pretty well with exact acosc1, and also with the expansion at zero below. The expansion at zero can be written as follows:
  6 KB (896 words) - 18:26, 30 July 2019
• BesselJ0
  ==Expansion at zero== The straightforward Taylor expansion at zero can be written as follows:
  6 KB (913 words) - 18:25, 30 July 2019
• Shoko function
  At small values of the argument, the [[Shoko function]] expands to the Taylor series as follows: Many Taylor coefficients of the expansion can be calculated with some [[Mathematica]] or [[Maple software]]; the seri
  10 KB (1,507 words) - 18:25, 30 July 2019
• SuZexTay0co.cin
  // Coefficients of the Taylor expansion at zero of function [[SuZex]].
  3 KB (107 words) - 15:01, 20 June 2013
• SuZex approximation
  ==Taylor expansion at zero== Fig.3. [[Taylor approximation]] (4) with 48 terms; \(!u\!+\!\mathrm i v= P_{48}(x\!+\!\math
  14 KB (2,037 words) - 18:25, 30 July 2019
• SuZex.cin
  // Coefficients of the Taylor expansion at zero of function [[SuZex]]. Furst ten values seem to be precize. ...bs(z) < 1.6 ) return SuZexTay0(z) ; // I made the Taylor expansion for this case
  12 KB (682 words) - 07:06, 1 December 2018

• File:Acosq1plotT.png ...parts the cubic polynomial corresponding to the truncation of the [[Taylor expansion]] at zero; [[Category:Taylor expansion]] (2,512 × 3,504 (379 KB)) - 09:41, 21 June 2013

• 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:SuZexMapSmall48c.png ...[complex map]]s for function [[SuZex]] and that for its truncated [[Taylor expansion]] at zero with last term of 48th power. (1,230 × 1,230 (970 KB)) - 09:43, 21 June 2013

• File:SuZexMapT.jpg ...bs(z) < 1.6 ) return SuZexTay0(z) ; // I made the Taylor expansion for this case ....) < 8.1 ) return suzex2008t12(z+12.) ; // I made the Taylor expansion for this case (4,576 × 4,542 (1.77 MB)) - 09:43, 21 June 2013

• File:SuZexo20testTjpg.jpg ...bs(z) < 1.6 ) return SuZexTay0(z) ; // I made the Taylor expansion for this case ....) < 8.1 ) return suzex2008t12(z+12.) ; // 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

• File:SuZexPlot511T.jpg ...bs(z) < 1.6 ) return SuZexTay0(z) ; // I made the Taylor expansion for this case ....) < 8.1 ) return suzex2008t12(z+12.) ; // I made the Taylor expansion for this case (1,055 × 2,292 (188 KB)) - 08:53, 1 December 2018

• File:SuZexTay0testT.png Agreement $A_{48}$ of the [[Taylor approximation]] of the [[SuZex]] at zero with highest term of 48th power; ...bs(z) < 1.6 ) return SuZexTay0(z) ; // I made the Taylor expansion for this case (1,230 × 1,230 (354 KB)) - 09:43, 21 June 2013

• File:SuZexTay2008deviTjpg.jpg ...bs(z) < 1.6 ) return SuZexTay0(z) ; // I made the Taylor expansion for this case ....) < 8.1 ) return suzex2008t12(z+12.) ; // I made the Taylor expansion for this case (4,576 × 4,542 (1.93 MB)) - 17:14, 25 September 2013

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