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  • File:AcosqplotT100.png
    [[ArcCosc]], [[ArcCosq]], [[Sazae-san functions]], [[Category:Holomorphic function]]
    (2,231 × 1,215 (152 KB)) - 09:41, 21 June 2013
  • File:ArcSeregaMapT.png
    Neither [[Serega function]] nor [[ArcSerega]] are [[holomorphic]]; the asterisk in the definition above denotes the [[complex conjugation]] // WARNING: non-holomorphic functions included!
    (1,312 × 1,312 (483 KB)) - 09:43, 21 June 2013
  • File:B271a.png
    The ArcTetration $\mathrm{ate}$ is inverse of [[tetration]] and holomorphic solution of the [[Abel equation]] 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:E1efig09abc1a150.png
    [[Category:Holomorphic functions]]
    (2,234 × 711 (883 KB)) - 08:34, 1 December 2018
  • File:Elutin1a4tori.jpg
    http://www.springerlink.com/content/u712vtp4122544x4/ D.Kouznetsov. Holomorphic extension of the logistic sequence. Moscow University Physics Bulletin, 201 [[Category:Mathematical functions]]
    (922 × 914 (62 KB)) - 09:38, 21 June 2013
  • File:QFactorialQexp.jpg
    Functions sqrt(!) , left, and sqrt(exp), right, in the complex plane. is a [[holomorphic function|holomorphic]] solution of the [[functional equation]]
    (800 × 399 (121 KB)) - 17:23, 11 July 2013
  • File:Superfactorea500.png
    [[Category:Holomorphic functions]]
    (575 × 748 (50 KB)) - 00:06, 29 February 2024
  • File:TaniaPlot.png
    [[Category:Inverse functions]] [[Category:Holomorphic functions]]
    (807 × 424 (16 KB)) - 09:39, 21 June 2013
  • File:Ackerplot.jpg
    For real base $b$, the ackermann is real-holomorphic, $A_{b,n}(z^*)=A_{b,n}(z)^*$. ...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
    For real base $b$, the ackermann is real-holomorphic, $A_{b,n}(z^*)=A_{b,n}(z)^*$. ...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: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) The similar image appears as Figure 1 in the First publication about real-holomorphic [[natural tetration]]
    (2,083 × 3,011 (1.72 MB)) - 08:29, 1 December 2018
  • File:Apow2ma4.jpg
    Two complex maps of the real-holomorphic [[abelpower]] functions, The two real–holomorphic solutions $G$ of the [[Abel equation]]
    (1,779 × 879 (616 KB)) - 08:29, 1 December 2018
  • File:Boyt.jpg
    ...of function sin are considered. The superfunction SuSin is constructed as holomorphic solution of the transfer equation sin(SuSin(z))=SuSin(z+1). The Abel functi 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
    ...of function sin are considered. The superfunction SuSin is constructed as holomorphic solution of the transfer equation sin(SuSin(z))=SuSin(z+1). The Abel functi ...of function sin are considered. The superfunction SuSin is constructed as holomorphic solution of the transfer equation sin(SuSin(z))=SuSin(z+1). The Abel functi
    (3,473 × 1,646 (467 KB)) - 08:31, 1 December 2018
  • File:Logic4T.jpg
    ...is case can be used for the testing of the numerical implementation of the holomorphic extension of the [[logistic sequence]], D.Kouznetsov. Holomorphic extension of the logistic sequence. Moscow University Physics Bulletin, 201
    (2,195 × 2,208 (1.66 MB)) - 08:42, 1 December 2018
  • File:Sqrt2sufuplot.png
    They are real-holomorphic solutions \(F\) of the transfer equation Along the real axis, functions
    (3,520 × 2,507 (408 KB)) - 10:11, 10 June 2022