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• Tania function
  According to the Axiom [[TORI]] number 6, the simplest among related functions should be considered as principal, at least for integer values of \(k\).
  27 KB (4,071 words) - 18:29, 16 July 2020
• LambertW function
  ...\(z\in \mathbb R : x \le -1/\mathrm e\). The principal branch is assigned number zero, LambertW[0,z]=LambertW[z]. ...\Im(f)\) are drawn in the \(x,y\) plane. The thick lines correspond to the integer values. The cut line corresponds to
  8 KB (1,107 words) - 18:26, 30 July 2019
• FFT
  where \(N\) is natural number; usually, \(2^n\) for some natural \(n\);<br> In such a way, \(k\) is integer number, \(0\le k < N\).
  6 KB (1,010 words) - 13:23, 24 December 2020
• Square root of exponential
  In the equation (3), the number \(c\) of iteration can no need to be integer; it can be fractional, irrational or even complex. ...] seems to be the first non-trivial function for which the non-trivial non-integer [[iteration]]s were reported, a "[[Holy Graal cup]]" <ref name="graal">http
  5 KB (750 words) - 18:25, 30 July 2019
• Iteration
  Similar notations, where the superscript is used to indicate the number of iterate is used also in [[quantum mechanics]] and the linear impulsive c ...cond argument is initial value of the iterations, and the last argument is number of iteration.
  14 KB (2,203 words) - 06:36, 20 July 2020
• Laws of arithmetics
  ...of arithmetics are the specific set of [[axiom]]s about operations with [[number]]s. Usually, the Laws of arithmetics are formulated for the [[natural number]]s.
  924 bytes (142 words) - 14:33, 20 June 2013
• Natural tetration
  ...in particular, it can be a fration, an irrational number of even a complex number. The non–integer iterations of exponential give the class of functions that grow faster than
  14 KB (1,972 words) - 02:22, 27 June 2020
• Iterated integral
  The simple case of natural \(n\) can be generalized for integer rational and even complex values of \(n\); such a generalization is at least for natural number \(n\). However, there are seductions to use such an expression also for com
  9 KB (1,321 words) - 18:26, 30 July 2019
• Election fraud
  ...[fuhrer]] and/or his party, that tis integer factor of 1% and, especially, integer factor go 5% is reported. In the case of [[Pamfilova peak]], the ...lure with robbery of protocols, the number of votes may greatly exceed the number of electors. This excess gives the estimate that or order of 46% of all bal
  33 KB (3,314 words) - 16:45, 9 September 2019
• ArcFactorial
  For some [[natural number|natural]] values of argument, ArcFactorial has natural values: At certain specific values of argument, ArcFactorial has half-integer values:
  3 KB (376 words) - 18:26, 30 July 2019
• Bessel transform
  ...\) is assumed to be real number; in many applications \(\nu\) is [[natural number]] or just zero. of integer order for propagating optical wave fields.
  8 KB (1,183 words) - 10:21, 20 July 2020
• Billion
  Also, [[billion]] can be interpreted as an [[integer number]]; its value may vary from \(10^{9}\) to \(10^{12}\).
  2 KB (334 words) - 18:25, 30 July 2019
• DCTIII
  For a given natural number \(N\), operator \(\mathrm{DCTIII}_N\) converts any array \(F\) of length \( For the simple and efficient implementation, \(N=2^q\) for some natural number \(q\). Note that the size of the arrays is for unity smaller than in the ca
  6 KB (825 words) - 18:25, 30 July 2019
• LogisticSequence
  where \(z\) is complex number and \(s\) is real number; usually it is assumed that \(s>1\). ...quence seems to be the most "natural" and most "physical" extension of the integer sequence considered in the literature; this extension appears at the constr
  7 KB (886 words) - 18:26, 30 July 2019
• Logistic operator
  These [[superfunction]] and [[abelfunction]] are used to plot the non-integer [[iterate]]s of the LogisticOperator; these iterates are shown with colored Often, the argument \(z\) is supposed to be a real number. In principle, it could be taken also from any set such that operations of
  6 KB (817 words) - 19:54, 5 August 2020
• ArcLambertW
  The number \(n\) of iteration hax no need to be integer. For several real values of \(n\), the \(n\)th iteration of [[zex]] by (8)
  3 KB (499 words) - 18:25, 30 July 2019
• SuZex approximation
  The series converges, and the increase of the number of terms taken into account extends the range of approximation. However, du ...P_{96}(z\!-\!n)~\)is used as approximation of \(\mathrm{SuZex}(z)\), with integer \(~n \!\approx\! \Re(z)\).
  14 KB (2,037 words) - 18:25, 30 July 2019
• Power function
  ...n some realizations, there may be some problems while one of arguments are integer and another one is complex. In some programming languages, including [[Math In some cases of integer \(a\) the function has specific names.
  15 KB (2,495 words) - 18:43, 30 July 2019
• Schroeder equation
  ...f equation (1), assuming that \(~s~\) and \(~g(z)~\) are not real negative number nor zero. This gives ...~\), \(~g~\) and \(~s~\), equation (9) provides a tool to evaluate the non-integer iterates of function \(T\).
  8 KB (1,239 words) - 11:32, 20 July 2020
• Fractional iterate
  [[Fractional iterate]] is concept used to construct non-integer iterates of functions. ...is called as \(~r\)th [[fractional iterate]], iff \(~r\!=\!m/n~\) for some integer numbers \(~m, n~\) and
  2 KB (272 words) - 18:25, 30 July 2019

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