Search results

• Complex map
  ...of a [[holomorphic function]] with the isolines of its real part and those of its imaginary part. ...ction, in any point, the isolines of the real part are orthogonal to those of the imaginary part; therefore the the complex maps have specific mesh-like
  2 KB (254 words) - 06:59, 1 December 2018
• Abelpower
  [[Abelpower]] appears [[inverse function]] of the [[superpower]] function. [[Abelpower]] is [[Abel function]] for the [[power function]], id est, that of the transfer function \(T(z)\!=\!z^a\)
  4 KB (621 words) - 14:01, 16 August 2025
• Superpower
  The two real-holomorphic superpower functions are considered here: For \(a\!=\!2\), the explicit plots of these two functions are shown in figure 1 at right.
  6 KB (903 words) - 18:44, 30 July 2019
• C++
  ...] is [[programming language]] characterized with simple syntax, efficiency of compilers and the resulting executable files. C++ is extension of the previously developed language '''C''', that allows to deal with [[compl
  4 KB (608 words) - 15:01, 20 June 2013
• Ctudent
  It is just integral of density of the [[Student Distribution]]: In most of the practical applications, both the \(\mathrm{Student}_n(x)\) and \(\mathr
  5 KB (621 words) - 08:20, 1 December 2025
• Julia set
  ...et of values in range of holomorphism of function, but out of holomorphism of some its integer iteration. Julia set is often defined with symbol \(J\) or \(\mathbb J\). The name of the function can be indicated either as the subscript or in the parenthesis
  4 KB (630 words) - 18:44, 30 July 2019
• LogisticSequence
  specific [[superfunction]] of the special case of quadratic [[transfer function]] called [[Logistic]] function or [[LogisticO ...ticSequence are shown in two figures at right. Below, the [[complex map]]s of function \(\mathrm{LogisticSequence}_s\) are shown for \(s\!=\!3\) and for
  7 KB (886 words) - 18:26, 30 July 2019
• ArcLambertW
  One of the inverse function of [[ArcLambertW]] is called [[LambertW]] In wide ranges of values of \(z\), the relations
  4 KB (646 words) - 16:58, 4 May 2025
• CosFT
  the sine transform [[SinFT]] of function \(f\) appears as \(g=\,\)[[SinFT]]\(f\) with rofmula At given number \(N\) of nodes,
  3 KB (468 words) - 18:47, 30 July 2019
• Mathematica
  ...upports this language, developed by the [[Wolfram corporation]] in the end of century 20 for simplification of mathematical expressions, solving equations, evaluation of functions, plotting graphics and other things that require some [[mathematics]].
  12 KB (1,901 words) - 18:43, 30 July 2019
• Logistic operator
  [[File:Logi1a345T300.png|600px|thumb|<small> Various iterates of \(T^c=\mathrm{LogisticOperator}_s\) for D.Kouznetsov. Holomorphic extension of the logistic sequence. Moscow University Physics Bulletin, 2010, No.2, p.91
  6 KB (817 words) - 19:54, 5 August 2020
• Nemtsov function
  ...emtsov function]] is a special kind of polynomial, suggested as an example of a [[transfer function]] in the book «[[Superfunctions]]» <ref name="book" [[Complex map]]s of \(\mathrm{nem}_q\) are shown in the left column of the figure below.
  17 KB (2,448 words) - 13:27, 7 December 2025
• Arcsin.cin
  ...[complex double]] routine in [[C++]] for evaluation of function [[ArcSin]] of complex argument. For some reason, the compiler recognises [[exp]], [[log]], [[sin]], [[cos]], of complex argument, but fails with asin and acos.
  4 KB (488 words) - 06:58, 1 December 2018
• Power function
  [[Power function]] ([[Степенная функция]]) is one of the primary [[elementary function]]s; ...eal plot of function \(T(z)\!=\!z^a\) is shown in Fig.1 for several values of \(a\).
  15 KB (2,495 words) - 18:43, 30 July 2019
• Exotic iteration
  ...[Regular iteration]] is not possible: in the leading term of the expansion of superfunction with exponentials, the increment \(k\!=\!\ln(T'(L)\) becomes However, even if the \(T'(L)\!=\!1\), construction of superfunction is possible. Few examples are considered in this article.
  11 KB (1,715 words) - 18:44, 30 July 2019
• Sandbox
  <small><center>\(y=\mathrm{tet}_b(x)\) versos \(x\) for various values of base \(b\).<br> https://www.amazon.co.jp/Superfunctions-Non-integer-holomorphic-functions-superfunctions/dp/6202672862<br>
  14 KB (2,018 words) - 12:07, 13 December 2025
• Tetration
  ...px}}<small><center>\(y=\mathrm{tet}_b(x)\) versus \(x\) for various values of base \(b\). &nbsp; [[Суперфункции]]<ref name="ru"/>,с.244,Ри https://www.amazon.co.jp/Superfunctions-Non-integer-holomorphic-functions-superfunctions/dp/6202672862<br>
  16 KB (2,243 words) - 16:50, 13 December 2025
• Superfunctions
  ...on]]s, [[superfunction]]s, and the non-integer [[iterate]]s of holomorphic functions. In particular, results for [[tetration]], [[arctetration]] and [[iterate]]s of [[exponential]] are presented.
  18 KB (2,338 words) - 21:02, 14 December 2025
• SuperFactorial
  '''SuperFactorial''', or "superfactorial", [[SuFac]] is [[superfunction]] of [[factorial]] constructed at its [[fixed point]] 2. Here, the upper index of a function indicates the number of [[iteration]]s.
  18 KB (2,279 words) - 16:08, 22 August 2025
• Regular Iteration
  A [[fractional iterate]] $\phi$ of an analytic function $f$ at fixpoint $a$ is called regular, iff $\phi$ is a ...rtrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.
  20 KB (3,010 words) - 18:11, 11 June 2022

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)