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• BesselJ1
  '''BesselJ1''' or \(J_1\) is [[Bessel function]] of first order; Function \(f=\mathrm{BesselJ1}\) satisfies the [[Bessel equation]]
  3 KB (439 words) - 18:26, 30 July 2019
• Holomorphic extension of the Collatz subsequence
  can be defined through the transfer function \(g\) of the Collatz sequence. For integer values of \(n\), the Collatx transfer function
  5 KB (798 words) - 18:25, 30 July 2019
• Base sqrt2
  Higher [[Ackermann function]]s to this base. The exponential is [[entire function|entire]] periodic function with period
  3 KB (557 words) - 18:46, 30 July 2019
• Conjecture on superfunctions
  ...rphic solution of the transfer equation sin(SuSin(z))=SuSin(z+1). The Abel function AuSin is constructed as solution of the Abel equation AuSin(sin(z))=AuSin(z D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.
  7 KB (1,031 words) - 03:16, 12 May 2021
• Sutran.cin
  ...mentation of function [[SuTra]], which is superfunction of the [[Trappmann function]] \(\mathrm{tra}(z)=z+\exp(z)\). ...ise that [[sutra.cin]], that evaluates the same function [[SuTra]] through function [[SuZex]]
  3 KB (351 words) - 18:48, 30 July 2019
• Nyquist theorem
  [[Nyquist theorem]] refers to representation of a function, continuous at least along the real axis, through the linear combination of at zero sinc is defined to be unity; then sinc appears to be [[entire function]].
  6 KB (944 words) - 18:48, 30 July 2019
• Trappmann function
  [[Trappmann function]] is defined with ...re elementary function. The Trappmann function is example of [[holomorphic function]] without [[fixed point]]s, suggested in year 2011 by [[Henryk Trappmann]]
  9 KB (1,320 words) - 11:38, 20 July 2020
• Sandbox
  ...given base \(b\), the tetration \(\operatorname{tet}_b\) is defined as the function satisfying the transfer equation A function \(F\) is a ''superexponential'' (a superfunction of \(T_b\)) if
  8 KB (1,129 words) - 00:20, 12 December 2025
• Logistic operator
  [[Logistic operator]] (or '''LogisticOperator''') is quadratic function of specific kind determined with the single parameter \(s\), which is usula ...(u\) or \(q\)). In such a way, \(\mathrm{LogisticOperator}_s\) is [[entire function]].
  6 KB (817 words) - 19:54, 5 August 2020
• SuTra
  [[SuTra]], or SuperTrappmann function is [[superfunction]] <ref> http://www.springerlink.com/content/qt3167123742 </ref> of the [[Trappmann function]], \(~\mathrm{tra}(z)=z+\exp(z)~\).
  9 KB (1,285 words) - 18:25, 30 July 2019
• LambertW function
  http://mathworld.wolfram.com/LambertW-Function.html Weisstein, Eric W. "Lambert W-Function." From MathWorld--A Wolfram Web Resource. </ref>, is solution \(W=W(z)\) of
  8 KB (1,107 words) - 18:26, 30 July 2019
• BesselJ0
  ...the '''[[Bessel function]] of zero order''' and also \(J_0\), is [[entire function]], solution of equation [[Complex map]] of function BesselJ0 is shown in figure at right. The short notation \(J_0=\mathrm{Bess
  6 KB (913 words) - 18:25, 30 July 2019
• LogisticSequence
  ...of the special case of quadratic [[transfer function]] called [[Logistic]] function or [[LogisticOperator]] ...Sequence are shown in two figures at right. Below, the [[complex map]]s of function \(\mathrm{LogisticSequence}_s\) are shown for \(s\!=\!3\) and for \(s\!=\!4
  7 KB (886 words) - 18:26, 30 July 2019
• Zooming equation
  where \(~T~\) is some given function such that \(T(0)\!=\!0\) and \(~K~\) is constant, that depends on \(T\). at least in some vicinity of zero, and \(~K\!=\!T'(0)~\). Function \(~f~\) is requested to built-up.
  10 KB (1,627 words) - 18:26, 30 July 2019
• Nori
  ...y of the real axis \(\Re(z\ge 0\)) can be expressed through the [[morinaga function]] mori: where \(j_0=\,\)[[BesselJ0]] is the zeroth [[bessel function]], and \(L=\mathrm{BesselJZero}[0,1]\approx 2.404825557695773\) is its firs
  13 KB (1,759 words) - 18:45, 30 July 2019
• Table of superfunctions
  For a given function \(T\), called [[transfer function]], the holomorphic solution \(F\) of [[Transfer equation]] The inverse function, id est, \(G=F^{-1}\) is called [[Abel function]] with respect to \(T\); it satisfies the [[Abel equation]]
  12 KB (1,661 words) - 19:16, 18 August 2025
• ArcTra
  ArcTra is inverse of the [[Trappmann function]]; \(\mathrm{ArcTra}=\mathrm{tra}^{-1}\), where [[ArcTra]] can be expressed through the [[Tania function]] as follows:
  10 KB (1,442 words) - 18:47, 30 July 2019
• Iteration
  ...([[итерация]]) is function, expressed as repetition of another (iterated) function, that may be called [[iterand]]. Any function by itself is considered as its first iteration.
  14 KB (2,203 words) - 06:36, 20 July 2020
• Kori
  [[kori]] function appears in the calculus of the loss in the [[pinhole waveguide]] in the [[p ...the [[Bessel mode]] to the propagated [[Bessel mode]] is expressed through function [[kori]].
  14 KB (1,943 words) - 18:48, 30 July 2019
• HIKARI Applied Mathematical Sciences
  D.Kouznetsov. Entire function with logarithmic asymptotic. Applied Mathematical Sciences, 2013, v.7, No.1
  3 KB (386 words) - 07:01, 1 December 2018

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