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- H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (2 KB (248 words) - 14:33, 20 June 2013
- The pair of functions \(\mathrm {tet}\) and \(\mathrm{ate}\) The non–integer iterations of exponential give the class of functions that grow faster than any polynomial but slower than any exponential.14 KB (1,972 words) - 02:22, 27 June 2020
- Velocities \(\vec v_n\) and momenta \(\vec p_n\) are supposed to be functions of [[time]], but, for the isolated system, \(\vec P\) is supposed to remain3 KB (488 words) - 18:25, 30 July 2019
- ...le from another is important), in analogy with property [[periodicity]] of functions in [[mathematical analysis]]. Each periodic process can be interpreted as [3 KB (464 words) - 14:33, 20 June 2013
- ...of coordinates is shown with red cross. The same grid is used for all the functions evaluated below.6 KB (954 words) - 18:27, 30 July 2019
- ...at moved through Vladlen Stepanov’s accounts. Doing so is important. The functions of Russia’s Interior Ministry and Tax Ministry have already been substant10 KB (1,455 words) - 18:26, 30 July 2019
- ...ed presentation and hard discussion of the superfunctions and the transfer functions of laser amplifiers (uniqueness of the superfunction, the range of applicab8 KB (1,147 words) - 18:44, 30 July 2019
- ...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 ( [[Category:Mathematical functions]]6 KB (312 words) - 18:33, 30 July 2019
- ...ay consider application of the fractional differentiation to some specific functions; for example, the polynomial or the exponential. Q4 What general class of functions could be differentiated fractionally be means of the idea contained in (1)?9 KB (1,321 words) - 18:26, 30 July 2019
- ...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 (7 KB (381 words) - 18:38, 30 July 2019
- ...le=Self-pulsing laser as oscillator Toda: Approximation through elementary functions|journal=[[Journal of Physics A]]|volume=40|pages=1–18| year=2007|doi=10.112 KB (1,757 words) - 07:01, 1 December 2018
- //Other functions defined below provide approximations for various parts of the complex plane9 KB (654 words) - 07:00, 1 December 2018
- [[Category:Special functions]]2 KB (59 words) - 18:33, 30 July 2019
- ...bot''' is human-created object that can perform some of complicated human functions in the automatic regime. ...anies that produce robots often pretend that their robots can perform some functions, described in science-fiction.5 KB (746 words) - 14:55, 20 June 2013
- ==Relation to other functions== ArcCos can be expressed through functions [[Arccosh]]:5 KB (754 words) - 18:47, 30 July 2019
- The notations of this article are not good. Many other similar functions should be described and implemented, anf theu should have similar names. Th For the corresponding inverse functions, the following articles should be loaded:<br>8 KB (1,211 words) - 18:25, 30 July 2019
- ==Relations to other functions== [[Category:Elementary functions]]9 KB (982 words) - 18:48, 30 July 2019
- Functions \(~y\!=\!\mathrm{coshc}(x)~\) and \(~y\!=\!\mathrm{coshc}'(x)~\) are shown4 KB (509 words) - 18:26, 30 July 2019
- Knowledge of these constants simplifies evaluation of functions [[ArcCosc]] and [[ArcCohc]]. ...Cosc]] as it it would be elementary function. It has sense to include such functions as [[Tetration]], [[ArcTetration]], [[SuperFactorial]], [[AbelFactorial]],8 KB (1,137 words) - 18:27, 30 July 2019
- ==Related functions== [[Trigonometriv functions]], [[cos]], [[sin]]4 KB (649 words) - 18:26, 30 July 2019
- ==[[Sazae-san functions]] and related constants== ...15 decimal digits are used in the numerical implementation of the related functions.4 KB (581 words) - 18:25, 30 July 2019
- [[File:SazaeconT.png|600px|right|thumb|Graphics of functions [[cohc]] and [[cosc]] ]] ...ma and singularities of functions [[cosc]] and [[coshc]] and their inverse functions:4 KB (495 words) - 18:47, 30 July 2019
- [[ArcCosc]], [[Cosc]], [[Sazae-san functions]], [[Guiding of waves between absorbing walls]] [[Category:Inverse functions]]4 KB (656 words) - 18:25, 30 July 2019
- through functions [[acosq]] (or [[ArcCosq]]) expressed with While the argument approaches zero, functions [[ArcCosc]] and [[ArcCosq]] approach \(\pi/2\), and the [[Tangent]] in defi2 KB (216 words) - 18:26, 30 July 2019
- ...inity of its branch points, acosc1 can be asymptotically approximated with functions below, shown also in the figure:6 KB (896 words) - 18:26, 30 July 2019
- at least for continuous functions \(f\) and \(g\). ...n the case of the [[Fourier transform]], the scale of the arguments of the functions \(f\) and \(g\) can be varied, defining the new function8 KB (1,183 words) - 10:21, 20 July 2020
- Along the real axis, BesselJ0 oscillates (like other [[Bessel]] functions). The zeros of are denoted with \(j_{0,n}\); where \(n\) is supposed to be6 KB (913 words) - 18:25, 30 July 2019
- [[Category:Sazae-san functions]]4 KB (563 words) - 18:27, 30 July 2019
- Functions are represented with7 KB (1,063 words) - 18:25, 30 July 2019
- 3 KB (394 words) - 18:26, 30 July 2019
- ...tion''' (or cylinder finction or cylindrical function) is class of special functions \(f\) satisfying equation Several cylindric functions have special names: [[BessleJ]] = J, [[BesselY]]=Y, [[BesselH]]=H, or, corr3 KB (388 words) - 18:26, 30 July 2019
- http://www.gnu.org/software/gsl/manual/html_node/Regular-Cylindrical-Bessel-Functions.html3 KB (439 words) - 18:26, 30 July 2019
- Many formulas about the Bessel functions below are borrowed from the handbook by [[Abramowirtz,Stegun]] Abramovitz, Stegun. Handbook on mathematical functions.13 KB (1,592 words) - 18:25, 30 July 2019
- The coordinates of each point are smooth functions of time. All velocities are differentiable functions, and the time derivative of velocity is called acceleration:4 KB (560 words) - 18:26, 30 July 2019
- defined on the set of functions \(f\) such that the integral below converges: At the set of continuous functions, defined for the positive values of the argument, the second iteration of t6 KB (915 words) - 18:26, 30 July 2019
- ...etimes the special font is used to avoid the confusion with parameters and functions.) For the continuous square-integrable functions, the discrete approximation with \(N\) points can be written with uniform m6 KB (1,032 words) - 18:48, 30 July 2019
- The name of the functions and sense of the arguments are chosen following notations by the [[Numerica The C++ numerical CosFourier transform of the self-Fourier function \(F(x)=\exp(-x^2/2)\) can be realized as follows:10 KB (1,447 words) - 18:27, 30 July 2019
- ...ed; explicit representation for all the coordinates in terms of elementary functions are suggested. Note that the couple (First and Second bodies) rotates with8 KB (1,036 words) - 18:25, 30 July 2019
- The name of the functions and sense of the arguments are chosen following notations by the [[Numerica10 KB (1,689 words) - 18:26, 30 July 2019
- ...the integrand is expressed only in terms of already known, id est, spedial functions), then this expression can be qualified as '''exact solution'''.2 KB (351 words) - 15:00, 20 June 2013
- The only functions can be differentiated, and the name of this function should be explicitly d are derivatives of functions \(X\) and \(Y\) with respect to the last argument. \(u\) has sense of the h12 KB (1,879 words) - 18:26, 30 July 2019
- // '''serega.cin''' is the numerical [[C++]] implementation of functions // Warining: non-holomorphic functions below!1 KB (265 words) - 15:00, 20 June 2013
- are derivatives of functions \(X\) and \(Y\) with respect to the last argument. In the implementation of ArcSerega, it is treated as pair of functions of pair of variables.5 KB (674 words) - 18:25, 30 July 2019
- ...quence and its inverse functions can be expressed in terms of [[elementary functions]], ...\mathrm {ArcLogisticSequence}_s\) are available. The complex maps of these functions for various \(s\) are suggested in <ref name="logi">7 KB (886 words) - 18:26, 30 July 2019
- ...is usually interpreted as operation of multiplication or [[combination of functions]].3 KB (380 words) - 18:25, 30 July 2019
- Many superfuncitons for the given transfer function exist; and many Abel functions exist too. That called ArcLogisticSequance seems to be the simplest one. Ac ...nown; the efficient algorithms for the evaluation are supplied. With these functions, the explicit plot of some iterations of the logistic operators are6 KB (817 words) - 19:54, 5 August 2020
- For this reason, both functions, [[Tania function]] and [[WrightOmega]] are used in [[TORI]]. [[Category:Holomorphic functions]]4 KB (610 words) - 10:22, 20 July 2020
- In the strip \(|\Im(z)|<\pi\), functions Keller and Keller\(_0\) are equivalent, \(\mathrm{Keller}(z)=\mathrm{Keller As the Keller is expressed through elementary functions, no special numerical implementation is required.10 KB (1,479 words) - 05:27, 16 December 2019
- ...ty of the real axis (and, in particular, for real values of the argument), functions [[Shoka function|Shoka]] and [[Shoko function|Shoko]] coincide. The [[Shoko function]] can be expressed through the elementary functions:10 KB (1,507 words) - 18:25, 30 July 2019
- ==Various inverse functions== For efficient comparison of various [[superfunction]]s \(F\) of the transfer functions \(T\) of realistic physical systems, the extension to the complex plane see3 KB (441 words) - 18:26, 30 July 2019
