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- ...function]] that expresses the [[fixed point]]s of [[logarithm]] to complex base. for base \(b\!=\!\exp(z)\).4 KB (572 words) - 20:10, 11 August 2020
- : \( \mathrm{Sinc}(z)= 1-\frac{z^2}{6}+\frac{z^4}{120}-\frac{z^6}{5040}+ : \(\!\!\!\!\!\!\!\! \mathrm{ArcSinc}(1\!-\!t)= \sqrt{6 t} \left(4 KB (563 words) - 18:27, 30 July 2019
- \( \!\!\!\!\!\!\!\!\! (1) ~ ~ ~ f''(z)+f'(z)/z+(1-\nu/z^2)f(x) =0\) f(x) \approx x^\nu \left( \frac{2^{-\nu}}{\mathrm{Factorial}(\nu)}+ O(x^2) \right)\)13 KB (1,592 words) - 18:25, 30 July 2019
- ...tion of the [[superfunction]] of the [[exponential]] to base \(b\!=\!\sqrt{2}\), constructed at the fixed point \(L\!=\!4\). 0.12022125769065893274e-1, 0.45849888965617461424e-2,1 KB (139 words) - 18:48, 30 July 2019
- ...tion of the [[Abel function]] of the [[exponential]] to base \(b\!=\!\sqrt{2}\), constructed at the fixed point \(L\!=\!4\). -0.587369764200886206e-2, 0.289686728710575713e-2,2 KB (163 words) - 18:47, 30 July 2019
- Consider [[logarithm]] to base \(~s~\) from both sides of equation (1), assuming that \(~s~\) and \(~g(z)~ (2) \(~ ~ ~ \log_s\Big(~ g\big( T(z)\big)~\Big) = 1 + \log_s\big(g(z)\big)~\)8 KB (1,239 words) - 11:32, 20 July 2020
- (2) \(~ ~ ~ g\big(T(z)\big)= K \, g(z) \) http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html10 KB (1,627 words) - 18:26, 30 July 2019
- [[File:Ack3a600.jpg|400px|thumb|Base \(b=\sqrt{2}\approx 1.41\)]] [[File:Ack3b600.jpg|400px|thumb|Henryk base, \(b=\exp(1/\mathrm e)\approx 1.44\)]]5 KB (761 words) - 12:00, 21 July 2020
- https://www.morebooks.de/store/gb/book/superfunctions/isbn/978-620-2-67286-3 [[File:978-620-2-67286-3-full.jpg|440px]]15 KB (2,166 words) - 20:33, 16 July 2023
- ...pg|200px|thumb|Thick green curve: \(y=\eta^x\); thin red curve: \(y=(\sqrt{2})^x\)]] [[Base e1e]] refers to the value of base \(b= \eta =\exp(1/\mathrm e)\approx 1.4446678610\)4 KB (559 words) - 17:10, 10 August 2020
- ...apT.png|300px|thumb|[[Complex map|Map]] of [[exponent]] to base \(b=\sqrt{2}\); lines of constant \(u\) and lines of constant \(v\) show ...00.jpg|300px|thumb|[[Complex map|Map]] of [[Logarithm]] to base \(b=\sqrt{2}\); lines of constant \(u\) and lines of constant \(v\) show3 KB (557 words) - 18:46, 30 July 2019
- </ref> and \(~y=\sin^n(\pi/2)-\sin^n(x)~\) with \(~n\!=\!100~\) http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html<br>7 KB (1,031 words) - 03:16, 12 May 2021
- Let \(~ T(z)=z+b z^2 + c z^3+..\) T[z_] = z + b z^2 + c z^3;11 KB (1,715 words) - 18:44, 30 July 2019
- http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html<br> ...H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.2 KB (344 words) - 07:02, 1 December 2018
- ...ansform, refers to the integral transform with kernel \(K(x,y)=\sqrt{\frac{2}{\pi}} \sin(xy)\); \(\displaystyle g(x)=\,\)[[SinFT]]\(f\,(x) \displaystyle =\sqrt{\frac{2}{\pi}} \int_0^\infty \sin(xy) \, f(y) \, \mathrm d y\)5 KB (807 words) - 18:44, 30 July 2019
- 2. Alternative representations of the function, relation of the function to o And kilogram be 2 lb.7 KB (991 words) - 18:48, 30 July 2019
- ...uggests 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 F21E(z)1 KB (109 words) - 18:48, 30 July 2019
- ...Sqrt2f21l.cin]] is code for evaluation of [[arctetration]] to base \(\sqrt{2}\) of complex argument. DB TcL[23]={1., //coeff. of expansion of exp(-q(z+1.2 ...) by powers of (2-F).1 KB (145 words) - 18:47, 30 July 2019
- ...r 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 F23E(z)2 KB (146 words) - 18:47, 30 July 2019
- ...or evaluation of real–holomorphic abelexponential to base \(b\!=\!\sqrt{2}\). //In order to evaluate \(\mathrm{tet}_{\sqrt{2}}(z)\), the routine should be called as F23L(z)2 KB (168 words) - 18:47, 30 July 2019
- ...Sqrt2f43e.cin]] is routine for evaluation of superexponent to base \(\sqrt{2}\) that approach 4 at \(-\infty\) and has value 3 at zero. 0.12022125769065893274e-1, -0.45849888965617461424e-2,1 KB (131 words) - 10:44, 24 June 2020
- ...[Sqrt2f43e.cin]] is routine for evaluarion of abelexponent to base \(\sqrt{2}\) that approach 4 at \(-\infty\) and has value zero at 3. -0.587369764200886206e-2, 0.289686728710575713e-2,1 KB (124 words) - 18:46, 30 July 2019
- ...at ecaluates the growing [[Abel function]] of the exponent to base \(\sqrt{2}\) -0.587369764200886206e-2, 0.289686728710575713e-2,1 KB (131 words) - 18:47, 30 July 2019
- ...ions. Bulletin (New Series) of the American Mathematical society, v.29, No.2 (1993) p.151-188.</ref><ref name="domsta"> ...l as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.15 KB (2,392 words) - 11:05, 20 July 2020
- D.Kouznetsov, H.Trappmann. Superfunctions and sqrt of Factorial. [[Tetration]] to base \( b\) appears as holomorphic solution \( F= \mathrm{tet}_b \)12 KB (1,732 words) - 14:01, 12 August 2020
- We say that the base \(b\) is in the [[Shell-Thron region]] if the sequence of values We say that the base \(b\) is in the [[Shell-Thron region]] if the sequence of values7 KB (1,082 words) - 07:03, 13 July 2020
- // superexponential to base \( \sqrt{2} \) 0.12022125769065893274e-1, 0.45849888965617461424e-2,1 KB (112 words) - 13:42, 7 July 2020
- \( N = \log_{10}(100/0.5) = \log_{10}(200) \approx 2.301029995664 \approx 2 \) ===Exercise 2===10 KB (1,491 words) - 18:09, 11 June 2022
- ...2srav.png|300px}}<small><center> \( y_1=\exp_{\sqrt{2},2}^{~1/2}(x) \) , \( y_2=\exp_{\sqrt{2},4}^{~1/2}(x) \) ,<br> and the deviation \(D = y_1-y_2\)</center></small></div>5 KB (712 words) - 08:18, 9 May 2024
