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  • File:ArcGamma.jpg
    [[Category:Mathematical functions]]
    (1,188 × 924 (156 KB)) - 08:29, 1 December 2018
  • File:Factorialz.jpg
    [[Category:Plots of functions]]
    (1,219 × 927 (479 KB)) - 08:35, 1 December 2018
  • File:FactoReal.jpg
    [[Category:plots of functions]]
    (915 × 1,310 (141 KB)) - 08:35, 1 December 2018
  • File:OneOverFactorial.jpg
    [[Category:Mathematical functions]]
    (1,244 × 949 (276 KB)) - 17:50, 20 June 2013
  • File:5kar.jpg
    ...in pees together with bear, showing the similarity and the distribution of functions in the russian [[tandem]].
    (438 × 640 (28 KB)) - 09:40, 21 June 2013
  • File:AbelFactorialMap.png
    [[Category:Abel functions]]
    (675 × 673 (120 KB)) - 08:28, 1 December 2018
  • File:AbelFactorialR.png
    [[Category:Abel functions]] [[Category:Inverse functions]]
    (1,060 × 705 (34 KB)) - 09:39, 21 June 2013
  • File:AcipmapTjpg.jpg
    ...a general case, the complex double function ACip5 should be called. other functions are good only for the special case.
    (1,759 × 1,746 (661 KB)) - 09:41, 21 June 2013
  • File:AcipmapTpng.png
    ...a general case, the complex double function ACip5 should be called. other functions are good only for the special case.
    (844 × 838 (199 KB)) - 09:41, 21 June 2013
  • File:AcomapT200.png
    [[Category:Elementary functions]]
    (2,345 × 2,328 (1.06 MB)) - 09:41, 21 June 2013
  • File:Acosc1mapT.png
    [[Cosc]], [[Arccosc]], Inverse funciton]], [[Sazae-san functions]], [[Sazae-san constants]]
    (1,759 × 1,746 (862 KB)) - 09:41, 21 June 2013
  • File:AcoscmapT300.png
    ...e [[plofu.cin]]. However, for different manuscripts and different kinds of functions, the different styles may be required.
    (3,517 × 3,492 (1.64 MB)) - 09:41, 21 June 2013
  • File:AcosqplotT100.png
    [[ArcCosc]], [[ArcCosq]], [[Sazae-san functions]], [[Category:Sazae-san functions]]
    (2,231 × 1,215 (152 KB)) - 09:41, 21 June 2013
  • File:AcosqqplotT.png
    through functions [[acosq]] (or [[ArcCosq]]); it is expressed as;
    (1,686 × 1,823 (148 KB)) - 09:41, 21 June 2013
  • File:ArcCipMapT.jpg
    ...a general case, the complex double function ACip5 should be called. other functions are good only for the special case.
    (1,759 × 1,746 (661 KB)) - 09:41, 21 June 2013
  • File:ArcSeregaMapT.png
    // WARNING: non-holomorphic functions included!
    (1,312 × 1,312 (483 KB)) - 09:43, 21 June 2013
  • File:ArcTaniaMap.png
    [[Category:Inverse functions]]
    (851 × 841 (626 KB)) - 08:30, 1 December 2018
  • File:ArcYulyaPlot100.png
    [[Category:Inverse functions]]
    (3,540 × 748 (220 KB)) - 09:39, 21 June 2013
  • File:AsimapT.png
    [[Category:Elementary functions]]
    (1,759 × 1,746 (746 KB)) - 09:41, 21 June 2013
  • File:AsincmapT.png
    [[Category:Inverse functions]]
    (1,759 × 1,746 (896 KB)) - 09:41, 21 June 2013
  • File:AsincplotT500.png
    Explicit plot of functions [[ArcSinc]] (thick blue curve) and [[ArcCosc]] (thin red curve): [[Category:Sazae-san functions]]
    (843 × 2,014 (184 KB)) - 09:41, 21 June 2013
  • File:AuZexLamPlotT.jpg
    [[Explicit plot]] of functions [[AuZex]] (thick black curve) and [[LambertW]] (thin red curve).
    (2,508 × 841 (169 KB)) - 08:30, 1 December 2018
  • File:B271a.png
    H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (
    (1,609 × 1,417 (506 KB)) - 08:30, 1 December 2018
  • File:Besselj1mapT080.png
    [[Category:Special functions]]
    (2,056 × 1,048 (1.72 MB)) - 09:42, 21 June 2013
  • File:Bessely0mapT064.png
    [[Category:Cylindric functions]]
    (1,462 × 745 (1.35 MB)) - 09:42, 21 June 2013
  • File:CoshcplotT.png
    Explicit plot of functions [[Coshc]] and [[Coshc']] for positive values of the argument. Functions $~y\!=\!\mathrm{coshc}(x)~$ and $~y\!=\!\mathrm{coshc}'(x)~$ are shown in t
    (465 × 851 (36 KB)) - 09:41, 21 June 2013
  • File:E1efig09abc1a150.png
    [[Category:Holomorphic functions]]
    (2,234 × 711 (883 KB)) - 08:34, 1 December 2018
  • File:Elutin1a4tori.jpg
    [[Category:Mathematical functions]]
    (922 × 914 (62 KB)) - 09:38, 21 June 2013
  • File:Esqrt2iterMapT.png
    the functions $F$ and $G$ are called $F_{4,5}$ and $F_{4,5}^{~-1}$.
    (1,092 × 1,080 (1.36 MB)) - 09:43, 21 June 2013
  • File:Expc.jpg
    [[Category:Mathematical functions]]
    (941 × 852 (48 KB)) - 18:39, 11 July 2013
  • File:ExpIte4T.jpg
    ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188.
    (1,673 × 1,673 (901 KB)) - 08:35, 1 December 2018
  • File:FourierExampleGauss16pol04Ta.png
    [[Explicit plot]] of the [[self-Fourier function]] and its discrete approximation. [[Category:Self-Fourier functions]]
    (2,134 × 470 (88 KB)) - 09:39, 21 June 2013
  • File:IterPowPlotT.png
    ...e can be expressed in the closed form through the same function. For other functions, such a representation may be not available. ...fic value $c\!=\!2$. The attempts to apply relations (6) to other transfer functions $T$ leads to confusions and errors.
    (2,093 × 2,093 (680 KB)) - 20:50, 28 September 2013
  • File:KellerDoyaT.png
    (661 × 881 (70 KB)) - 08:39, 1 December 2018
  • File:Logi1a345T300.png
    ...on-integer iterates of the [[logisticOperator]] are calculated through the functions [[LogisticSequence]] and [[ArcLogisticSequence]] with
    (1,636 × 565 (184 KB)) - 08:41, 1 December 2018
  • File:Modeabso25T.png
    Parameters $p$, $q$ and $r$ expressed through functions [[ArcCosq]]=[[acosq]] and [[ArcCosqq]] as follows:
    (2,657 × 905 (262 KB)) - 09:41, 21 June 2013
  • File:Plog4.png
    [[Category:Mathematical functions]]
    (307 × 432 (13 KB)) - 09:38, 21 June 2013
  • File:PowIteT.jpg
    ...e can be expressed in the closed form through the same function. For other functions, such a representation may be not available.
    (2,093 × 2,093 (1.01 MB)) - 08:46, 1 December 2018
  • File:QFactorialQexp.jpg
    Functions sqrt(!) , left, and sqrt(exp), right, in the complex plane. The corresponding functions <math>S</math> are, respectively, [[SuperFactorial]], left, and
    (800 × 399 (121 KB)) - 17:23, 11 July 2013
  • File:SazaeconT.png
    Graphics of functions [[Cohc]] and [[Cosc]]. Meanings of constants [[Sazae]], [[Tarao]], [[Fune]]
    (2,118 × 1,682 (216 KB)) - 09:41, 21 June 2013
  • File:SelfCosFTt200.png
    Two self-fourier functions and their discrete representations and their discrete [[CosFourier]] transf These functions are shown with dotted lines.
    (1,467 × 637 (100 KB)) - 09:42, 21 June 2013
  • File:SquareRootOfFactorial.png
    Graphical representation of the [[Square root of factorial]]: functions<br>
    (538 × 1,050 (34 KB)) - 09:39, 21 June 2013
  • File:Superfactocomple1.png
    [[Category:Mathematical functions]]
    (706 × 706 (172 KB)) - 00:10, 29 February 2024
  • File:Superfactorea500.png
    [[Category:Holomorphic functions]]
    (575 × 748 (50 KB)) - 00:06, 29 February 2024
  • File:TaniaBigMap.png
    [[Category:Approximation of functions]]
    (851 × 841 (654 KB)) - 08:53, 1 December 2018
  • File:TaniaContourPlot100.png
    [[Category:Inverse functions]]
    (1,182 × 1,168 (931 KB)) - 08:53, 1 December 2018
  • File:TaniaPlot.png
    [[Category:Inverse functions]] [[Category:Holomorphic functions]]
    (807 × 424 (16 KB)) - 09:39, 21 June 2013
  • File:Tet10bxr.jpg
    [[Category:Mathematical functions]]
    (2,491 × 1,952 (236 KB)) - 08:53, 1 December 2018
  • File:TetPlotU.png
    $y\!=\!x\!+\!1$. The difference between these two functions, scaled with factor 10, id est, $y=10\Big( \mathrm{tet}(x)-(x+1)\Big)$, is
    (838 × 2,088 (124 KB)) - 08:53, 1 December 2018
  • File:Tetreal10bx10d.png
    [[Category:Mathematical functions]]
    (2,192 × 2,026 (436 KB)) - 13:56, 5 August 2020
  • File:Tetreal2215.gif
    [[Category:Mathematical functions]]
    (876 × 881 (111 KB)) - 09:38, 21 June 2013
  • File:Tetreal2215.jpg
    // The functions defined in [[conto.cin]] and [[ado.cin]] should be downloaded for the compo
    (876 × 881 (130 KB)) - 09:38, 21 June 2013
  • File:TodaShow.png
    ...laser as oscillator Toda: approximation of the solution through elementary functions -- J. Phys. A: 40, 2107-2124 (2007).
    (1,707 × 317 (155 KB)) - 09:39, 21 June 2013
  • File:Exp1mapT200.jpg
    ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188.
    (2,281 × 1,179 (1.14 MB)) - 12:37, 28 July 2013
  • File:Exp09mapT200.jpg
    ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188.
    (2,281 × 1,179 (1.23 MB)) - 12:28, 28 July 2013
  • File:Exm01mapT200.jpg
    The complex double implementations [[FSEXP]] and [[FSLOG]] of these functions are used in the [[C++]] code below. ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188.
    (2,281 × 1,179 (834 KB)) - 12:52, 28 July 2013
  • File:Exm05mapT200.jpg
    ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188.
    (2,281 × 1,179 (705 KB)) - 12:54, 28 July 2013
  • File:Exm09mapT200.jpg
    ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188.
    (2,281 × 1,179 (560 KB)) - 12:56, 28 July 2013
  • File:Exm1mapT200.jpg
    ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188.
    (2,281 × 1,179 (544 KB)) - 12:47, 28 July 2013
  • File:2014.12.26rubleDollar.png
    and the approximations with elementary functions. where $M$ is total number of experimental data. Approximating functions are specified below:
    (1,502 × 651 (246 KB)) - 08:26, 1 December 2018
  • 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 2018
  • File: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 2018
  • File: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 2018
  • File: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 2018
  • File:2014specula.png
    Other curves correspond to the approximations with elementary functions.
    (1,502 × 651 (177 KB)) - 08:26, 1 December 2018
  • File: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 2018
  • File: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 2018
  • File: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 2018
  • File:Acker2t400.jpg
    (3,555 × 5,588 (1.09 MB)) - 08:28, 1 December 2018
  • File: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 2018
  • File: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 2018
  • File:Amosmap.jpg
    (1,726 × 1,718 (396 KB)) - 08:29, 1 December 2018
  • File: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 2018
  • File: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 2018
  • File:Anka616map.jpg
    where [[zex]] is elementary functions, $\mathrm{zex}(z)=z\,\exp(z)$
    (2,641 × 2,625 (1.48 MB)) - 08:29, 1 December 2018
  • File: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 2018
  • File:Aupow2map.jpg
    [[Category:Abel functions]]
    (2,175 × 2,158 (906 KB)) - 08:30, 1 December 2018
  • File:AuPow2Plot.jpg
    Explicit plof of two [[abelpower]] functions:
    (1,577 × 1,469 (219 KB)) - 08:30, 1 December 2018
  • File: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 2018
  • File: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
  • File:Facite.jpg
    For non–integer value sof $n$, the iterate is expressed through functions
    (2,092 × 2,092 (799 KB)) - 08:35, 1 December 2018
  • File:Hermigaaplot.jpg
    The approximations are build with functions [[amos]] that
    (1,672 × 477 (247 KB)) - 08:37, 1 December 2018
  • File:Hermigaplot.jpg
    (1,672 × 435 (160 KB)) - 08:37, 1 December 2018
  • File:Logic4T.jpg
    can be expressed in terms of elementary functions; this case can be used for the testing of the numerical implementation of t
    (2,195 × 2,208 (1.66 MB)) - 08:42, 1 December 2018
  • File:Magaplot300.jpg
    [[Explicit plot]] of function [[maga]] and related functions.
    (4,234 × 896 (401 KB)) - 08:42, 1 December 2018
  • File:MagaplotFragment.jpg
    [[Explicit plot]] of function [[maga]] and related functions.
    (1,743 × 896 (245 KB)) - 08:42, 1 December 2018
  • File:Moriplot300.jpg
    fprintf(o,".008 W 0 0 0 RGB S\n"); // this is agreement of functions morin and mori0; important at the testing.
    (2,366 × 572 (139 KB)) - 08:43, 1 December 2018
  • File:MoriplotFragment.jpg
    fprintf(o,".008 W 0 0 0 RGB S\n"); // this is agreement of functions morin and mori0; important at the testing.
    (1,917 × 514 (133 KB)) - 08:43, 1 December 2018
  • File:Nem1hht.jpg
    is expressed through functions [[SuNem]] and [[AuNem]].
    (759 × 747 (79 KB)) - 08:44, 1 December 2018
  • File:Nembrant.jpg
    ...onstruction of [[exotic iterate]]s; they can be constructed for asymmetric functions too.
    (361 × 871 (65 KB)) - 08:44, 1 December 2018
  • File:Norifit76fragment.jpg
    where functions nori and kori are evaluated through the straightforward definitions using t For reference, at the bottom, functions [[nori]] and [[kori]], scaled with factor 10, are shown with green and red
    (967 × 448 (155 KB)) - 08:44, 1 December 2018
  • File:Norifit76plot.jpg
    where functions nori and kori are evaluated through the straightforward definitions using t For reference, at the bottom, functions [[nori]] and [[kori]], scaled with factor 10, are shown with green and red
    (1,070 × 448 (168 KB)) - 08:44, 1 December 2018
  • File:QQFacMT.jpg
    The half iterate is evaluatef through functions [[SuFac]] and [[AuFac]]:
    (885 × 868 (437 KB)) - 08:48, 1 December 2018
  • File:Ruble85210a.png
    ...Currency band and the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 838
    (1,519 × 689 (217 KB)) - 08:50, 1 December 2018
  • File:Sqrt2sufuplot.png
    Along the real axis, functions
    (3,520 × 2,507 (408 KB)) - 10:11, 10 June 2022
  • File:Sufact.png
    [[Explicit plot]] of functions [[Factorial]] and [[SuFac]]:
    (1,677 × 2,191 (224 KB)) - 08:53, 1 December 2018
  • File:Sutralomap.jpg
    with two its approximations with entire functions,
    (2,533 × 1,254 (1.26 MB)) - 08:53, 1 December 2018
  • File:Vladi07.jpg
    Maps of agreement of approximations of natural [[tetration]] with elementary functions [[fima]] and [[maclo]], used in the implementation [[fsexp.cin]].
    (741 × 383 (100 KB)) - 08:56, 1 December 2018
  • File:Vladi08.jpg
    Agreement of approximations of tetration by elementary functions with the original representation through the Cauchi integral is shown in th
    (787 × 375 (117 KB)) - 08:56, 1 December 2018
  • File:ZexPlot.png
    [[Category:Inverse functions]] [[Category:Special functions]]
    (408 × 402 (10 KB)) - 08:57, 1 December 2018
  • File:2021.12.07.CovidRussiaForecast.png
    ...d blue curves show the pessimistic and optimistic extrapolation with power functions
    (1,706 × 841 (314 KB)) - 11:35, 7 December 2021
  • File:Student5map.png
    Let us cover all functions used in the research
    (1,706 × 1,690 (154 KB)) - 09:18, 10 May 2024
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