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File:2014.12.31rudo.png D.Kouznetsov. Fitting of economical data with elementary functions: rouble versus dollar in 2014. In preparation, 2015.(1,452 × 684 (190 KB)) - 08:26, 1 December 2018File:2014ruble15t.png ...he abscissa axis). Totally, 7 parameters are used to approximate the three functions. ...invited to construct better approximations for the same data with special functions (less parameters or less mean-square deviation).(693 × 680 (110 KB)) - 08:26, 1 December 2018File:2014rubleDollar2param.png ...Currency band and the approximations: Fitting of rouble with 3-parametric functions. 2015, under consideration.(1,527 × 1,004 (232 KB)) - 08:26, 1 December 2018File:2014rubleDollar3param.png In the way mentioned above, the following four functions $f$ are considered and plotted: For these functions, the mean square deviations is of order of 10.(1,273 × 837 (294 KB)) - 08:26, 1 December 2018File:2014specula.png Other curves correspond to the approximations with elementary functions.(1,502 × 651 (177 KB)) - 08:26, 1 December 2018File:2015ruble2.jpg ...Currency band and the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 838(1,726 × 709 (248 KB)) - 08:26, 1 December 2018File:2015ruble3.jpg ...Currency band and the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 838(1,726 × 684 (266 KB)) - 08:26, 1 December 2018File:2016ruble1.jpg ...Currency band and the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 838(2,764 × 684 (414 KB)) - 08:27, 1 December 2018File:Acker2t400.jpg (3,555 × 5,588 (1.09 MB)) - 08:28, 1 December 2018File:Ackerplot.jpg ...t/u7327836m2850246/ H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 ((2,800 × 4,477 (726 KB)) - 08:28, 1 December 2018File:Ackerplot400.jpg ...t/u7327836m2850246/ H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 ((3,355 × 4,477 (805 KB)) - 08:29, 1 December 2018File:Amosmap.jpg (1,726 × 1,718 (396 KB)) - 08:29, 1 December 2018File:Analuxp01t400.jpg ...this figure, $u$ and $v$ are [[logamplitude]] and [[phase]] of the plotted functions; not the real and imaginary parts, as usually. ...power and ultra exponential functions”. Integral Transforms and Special Functions 17 (8), 549-558 (2006)(2,083 × 3,011 (1.67 MB)) - 08:29, 1 December 2018File:Analuxp01u400.jpg ...power and ultra exponential functions”. Integral Transforms and Special Functions 17 (8), 549-558 (2006) Functions $\mathrm{fit}_2$ and $\mathrm{fit}_3$ above provide the key. I used to chec(2,083 × 3,011 (1.72 MB)) - 08:29, 1 December 2018File:Anka616map.jpg where [[zex]] is elementary functions, $\mathrm{zex}(z)=z\,\exp(z)$(2,641 × 2,625 (1.48 MB)) - 08:29, 1 December 2018File:Apow2ma4.jpg Two complex maps of the real-holomorphic [[abelpower]] functions, ...ined adding to the function some periodic function with period unity. Such functions show fast (at least exponential) growth in the imaginary direction; the abe(1,779 × 879 (616 KB)) - 08:29, 1 December 2018File:Aupow2map.jpg [[Category:Abel functions]](2,175 × 2,158 (906 KB)) - 08:30, 1 December 2018File:AuPow2Plot.jpg Explicit plof of two [[abelpower]] functions:(1,577 × 1,469 (219 KB)) - 08:30, 1 December 2018File:Boyt.jpg Super sin and the Abel sin functions, id est, [[SuSin]] and [[AuSin]], are used to evaluate the high iteration o(5,105 × 2,449 (1.17 MB)) - 08:31, 1 December 2018File:Boyt100.jpg Super sin and the Abel sin functions, id est, [[SuSin]] and [[AuSin]], can be used to evaluate the iteration of(3,473 × 1,646 (467 KB)) - 08:31, 1 December 2018