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- [[File:AuTraMapT.jpg|400px|thumb|\(u\!+\!\mathrm i v= \mathrm{AuTra}(x\!+\!\mathrm i y)\)]] [[File:AuTraPlotT.jpg|200px|thumb|\(y= \mathrm{AuTra}(x)\)]]6 KB (1,009 words) - 18:48, 30 July 2019
Page text matches
- [[AuTra]]4 KB (547 words) - 23:16, 24 August 2020
- |\(\mathrm{AuTra}(z)\!=\!\mathrm{AuZex}\! \big(\exp(z)\big)\! \) | [[Trappmann function]], [[SuTra]], [[AuTra]] <ref>11 KB (1,565 words) - 18:26, 30 July 2019
- \(~T^n(z)\!=\!\mathrm{tra}^n(z)\!=\! \mathrm{SuTra}\Big(n\!+\!\mathrm{AuTra}(z)\Big)~\) <!--[[Henryk function]] SuTra and the [[ArcHenryk function]] AuTra , !-->14 KB (2,203 words) - 06:36, 20 July 2020
- Name [[SuTra]] is suggested for the [[superfunction]] and name [[AuTra]] is suggested for the [[Abel function]]. ...ties of function '''Tra''' is described, and properties of [[SuTra]] and [[AuTra]] are mentioned.9 KB (1,320 words) - 11:38, 20 July 2020
- The inverse function of SuTra, id est, [[AuTra]]\(=\)SuTra\(^{-1}\), satisfies the [[Abel equation]] \(\mathrm{AuTra}(\mathrm{tra}(z))=\mathrm{AuTra}(z) + 1\)9 KB (1,285 words) - 18:25, 30 July 2019
- ...he Trappmann function [[tra]]\((z)=z+\mathrm e^z\). The inverse function [[AuTra]], id est, the [[Abel function]] for Trappmann function, requires the ArcTr ...ArcTra. In order to perform the numerical check of the conjectures about [[AuTra]], the efficient (fast, robust and precise) implementation of [[ArcTra]] is10 KB (1,442 words) - 18:47, 30 July 2019
- [[File:AuTraMapT.jpg|400px|thumb|\(u\!+\!\mathrm i v= \mathrm{AuTra}(x\!+\!\mathrm i y)\)]] [[File:AuTraPlotT.jpg|200px|thumb|\(y= \mathrm{AuTra}(x)\)]]6 KB (1,009 words) - 18:48, 30 July 2019
- // [[AuTra.cin]] is [[C++]] implementation of function [[AuTra]], id est, the [[Abel function]] dor the [[Trappmann function]] z_type autra(z_type z) { DB x,y,t; x=Re(z); y=fabs(Im(z));1 KB (197 words) - 15:03, 20 June 2013
File:AuTraMapT.jpg [[Complex map]] of function [[AuTra]], $u\!+\!i v\!=\! \mathrm{AuTra}(x\!+\!\mathrm i y)$ [[AuTra]] is [[Abel function]] of the [[Trappmann function]] $\mathrm{tra}(z)\!=\!z(4,367 × 4,317 (1.82 MB)) - 08:30, 1 December 2018File:AuTraPlotT.jpg [[Explicit plot]] of funciton [[AuTra]] of real argument. AuTra is the [[Abel function]] for the [[Trappmann function]](1,678 × 1,262 (172 KB)) - 08:30, 1 December 2018File:TraItT.jpg [[Category:Autra]](1,258 × 1,258 (604 KB)) - 08:54, 1 December 2018File:Autran0m10map64t.jpg [[AuTra]] z_type autra(z_type z) { if(fabs(Im(z))<M_PI) return auzex(exp(z));(1,254 × 1,670 (440 KB)) - 08:30, 1 December 2018File:Autran0m9tes64t.jpg [[AuTra]] z_type autra(z_type z) { if(fabs(Im(z))<M_PI) return auzex(exp(z));(1,254 × 1,670 (427 KB)) - 08:30, 1 December 2018File:Autran9tes20t1.jpg [[Agreement]] map for the numerical implementation of function [[AuTra]]; [[Category:Autra]](4,366 × 4,316 (1.68 MB)) - 08:30, 1 December 2018File:Autraplot.jpg Explicit plot of function [[AuTra]] and two its asymptotics. //DO(m,740){x=-1.25 +.02*m; y=Re(autra(x)); if(m==0) M(x,y) else L(x,y) if(x>6.03||y>6.01) break;} fprintf(o,".03(842 × 855 (99 KB)) - 08:30, 1 December 2018File:SutranmapTb.jpg [[Category:AuTra]](4,175 × 4,175 (1.75 MB)) - 08:53, 1 December 2018- The map of approximation of AuTra with the truncated expansion with 40 terms is shown in the figure that is n5 KB (761 words) - 18:48, 30 July 2019
- [[AuTra]],7 KB (991 words) - 18:48, 30 July 2019
- ...rm{AuTra}(z)\) убывает экспоненциально || \(|\mathrm{AuTra}(z)|\) растёт экспоненциально ...athrm{AuTra}(z)\Big)\) || \(\mathrm{tra}^n(z)=\mathrm{SuTra}\Big(n+\mathrm{AuTra}(z)\Big)\)19 KB (1,132 words) - 20:36, 16 July 2023