# Search results

• [[File:Ackerplot.jpg|400px|thumb|Tetration to base e (dashed) compared to other [[Ackermann function]]s]] '''Tetration''' (or Tetrational) $${\rm tet}_b$$ to base $$b \in \mathbb R$$, $$b\!>1$$<br>
21 KB (3,127 words) - 13:12, 5 August 2020
• ...ansfer equation]], the [[Abel equation]]; the transfer function is assumed to be given function that appear in these equations. The solutions of these eq ...r a given transfer function, the additional restrictions should be applied to make the [[superfunction]] and the [[Abel function]] unique
11 KB (1,644 words) - 06:33, 20 July 2020
• // showing the [[complex map]] of [[ArcTetration]] to base e. fprintf(o,"46 45 translate\n 10 10 scale\n");
3 KB (529 words) - 14:32, 20 June 2013
• ...aniaT.png|350px|right|thumb| Comparison of [[Tania function]] (thin curve) to the [[Shoka function]] (thick curve) for real values of the argument]] ...maginary axis and then along the straight line (parallel to the real axis) to the point $$z$$.
27 KB (4,071 words) - 18:29, 16 July 2020
• ...for comparison of superfunctions $$F$$ for various cases, it is convenient to keep relation $$F(0)=1$$ (as it is accepted for [[tetration]], which is [[superfunction]] of [[exponential]]); for this reason, the [[T
19 KB (2,778 words) - 10:17, 20 July 2020
• is called [[superfunction]] with respect to $$T$$. ...se function, id est, $$G=F^{-1}$$ is called [[Abel function]] with respect to $$T$$; it satisfies the [[Abel equation]]
11 KB (1,565 words) - 18:26, 30 July 2019
• The zeroth iteration of any non-trivial function is supposed to be [[Identity function]]. Similar notations, where the superscript is used to indicate the number of iterate is used also in [[quantum mechanics]] and th
14 KB (2,203 words) - 06:36, 20 July 2020
• $$\mathrm{tet}(x),\mathrm e^x,10(\mathrm{tet}(x)-(x\!+\!1))$$ [[Natural tetration]] is [[tetration]] to base $$\mathrm e=\exp(1)\approx 1.71~$$.
14 KB (1,972 words) - 02:22, 27 June 2020
• ...g|500px]]<small> Explicit plot of real and imaginary parts of tetration to base $$b\!=\!s$$</small> [[File:Shelima600.png|500px]]<small>Distribution of tetration to $$b\!=\!s$$ along the imaginary axis</small>
5 KB (707 words) - 21:33, 13 July 2020
• The specific choice of the contour allows to express values f(t) through the left hans side of (9) with the Transfer equ A. integration along the line $$\Re(t)=1$$ from $$t = 1−\mathrm i A$$ to $$t = 1+\mathrm i A$$,<br>
6 KB (987 words) - 10:20, 20 July 2020
• ...imations of [[SuZex]] with elementary functions. All the maps are supposed to be displayed in the same scale. Also, it is assumed that the solution $$F=\mathrm{SuZex}$$ decays to the stationary point 0 of the transfer function $$T$$ by (1) at infinity, e
14 KB (2,037 words) - 18:25, 30 July 2019
• ...[[F2048ten.inc]] defines the approximations of [[tetration]] to base $$b=10$$ along the imaginary axis at the interval (-20,20) in 2048 nodes of the qu // perhaps, Aten=20, and NPO =2048; NPO is supposed to be defined in GLxw.
89 KB (7,127 words) - 18:46, 30 July 2019
• ...rking directory) and the [[Transfer equation]] for the exponential to base 10 as [[transfer function]]. DB Lten=log(10.);
2 KB (287 words) - 15:03, 20 June 2013
• In particular, results for [[tetration]], [[arctetration]] and [[iterate]]s of [[exponential]] are presented, ISB Superfunctions: Non-integer iterates of holomorphic functions. Tetration and other superfunctions. Formulas,algorithms,tables,graphics Paperback...
14 KB (1,928 words) - 13:08, 12 January 2021
• [[Base e1e]] refers to the value of base $$b= \eta =\exp(1/\mathrm e)\approx 1.4446678610$$ ...corresponding [[exponential]], [[SuperExponential]] (in particular, the [[tetration]]) and the inverse functions.
4 KB (559 words) - 17:10, 10 August 2020
• // [[e1etf.cin]] is routine that evaluates [[tetration to Henryk base]] $$\eta=\exp(1/\mathrm e)$$. s[3]= t*(t*(t- 5/ 2.)+ 5/ 2.)- 7/10.;
2 KB (203 words) - 18:48, 30 July 2019
• // [[Sqrt2f21e.cin]] suggests routine F21E for evaluation of [[tetration]] to base $$b\!=\!\sqrt{2}$$. //In order to evaluate $$\mathrm{tet}_{\sqrt{2}}(z)$$, the routine should be called as F
1 KB (109 words) - 18:48, 30 July 2019
• ...sts routine F21E for evaluation of real–holomorphic superexponential to base $$b\!=\!\sqrt{2}$$. //In order to evaluate $$\mathrm{tet}_{\sqrt{2}}(z)$$, the routine should be called as F
2 KB (146 words) - 18:47, 30 July 2019
• ==Example with [[tetration]] to integer base for integer arguments== Is $$Y$$ an integer factor of 10?
3 KB (338 words) - 09:54, 14 January 2020
• ...tsova theorem]] refers to residual of division of [[tetration]] to integer base by any integer number. Here symbol tet veters to [[tetration]]. The base is indicated as subscript.
1 KB (150 words) - 20:23, 23 January 2020

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)