Search results
Create the page "Self-Fourier functions" on this wiki! See also the search results found.
Page title matches
- [[Algebra of one-dimensional generalized functions]] by [[Yurii Shirokov]] appears in but the main ideas of the non–commutative generalized functions still need to be applied in the [[Filed Theory]].38 KB (6,232 words) - 18:46, 30 July 2019
Page text matches
- In particular relation (1) makes it possible to approximate two functions of frequency, emission and absorption cross sections, with single fit16 KB (2,521 words) - 15:13, 17 June 2020
- ...le family gathered on the central terrace, to perform the custom of living functions. However, Jiri was already sitting at the computer and doing something on t ...usual motive for participation in tenders for the execution of government functions."135 KB (24,381 words) - 13:33, 30 October 2020
- Abramowitz and Stegun: Handbook of Mathematical Functions.8 KB (1,403 words) - 14:24, 20 June 2013
- ....Stegun: Handbook of Mathematical Functions. 6. Gamma Function and Related Functions (2010) ...r <math>z</math>, the integral can be expressed in terms of the elementary functions.27 KB (3,925 words) - 18:26, 30 July 2019
- H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 ( ...e requirements of the [[computational mathematics]] in the rapidly growing functions; if not, the superfunction of tetration, id est, [[pentation]] (\(\mathrm {21 KB (3,175 words) - 23:37, 2 May 2021
- // The functions defined in [[conto.cin]] and [[ado.cin]] should be downloaded for the compo [[Category:Mathematical functions]]6 KB (1,030 words) - 18:48, 30 July 2019
- [[Category:Mathematical functions]]4 KB (493 words) - 18:48, 30 July 2019
- http://www.automatedtrader.net/real-time-news/72114/japan-update-some-functions-to-resume-at-fukushima-reactor-2 Japan Update: Some Functions to Resume at Fukushima Reactor 2. 21 March 2011 04:11 am. <i>146 KB (19,835 words) - 18:25, 30 July 2019
- H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 ( [[Image:QFactorialQexp.jpg|400px|right|thumb|Complex maps of functions [[square root of factorial]], left, and \(\sqrt{\exp}\), right.]]14 KB (2,275 words) - 18:25, 30 July 2019
- ...authority. The state needs to stop thinking it has the right to non-state functions such as controlling enterprise.92 KB (14,748 words) - 18:44, 30 July 2019
- In particular, the [[Ackernann functions]] and [[tetration]] can be interpreted in terms of [[superfunction]]s. ...ns came from the application to the evaluation of fractional iterations of functions.25 KB (3,622 words) - 08:35, 3 May 2021
- [[File:Penplot.jpg|300px|thumb|\(y=\mathrm{pen}(x)\) and related functions.]]7 KB (1,090 words) - 18:49, 30 July 2019
- H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 ( H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (13 KB (1,766 words) - 18:43, 30 July 2019
- The Abel theorem above seems to have nothing to do with the [[Abel functions]] nor the [[Abel equations]]. The references about original works by Abel about the [[Abel functions]] are wanted; they should be cited in the articles [[superfunction]] and [[2 KB (320 words) - 18:25, 30 July 2019
- ...e.org/tetrationforum/index.php (dedicated to the [[tetration]] and similar functions).6 KB (899 words) - 07:07, 1 December 2018
- [[Category:Mathematical functions]]5 KB (798 words) - 18:25, 30 July 2019
- ...he [[Abel function]] is considered as principal, as it allows to deal with functions that have no real fixed points (and, perhaps, no fixed points at all). ...periodicity may have the [[Abel function]] $~G=F^{-1}~$. However, the Abel functions, corresponding at different [fixed points]] have no need to have the20 KB (3,010 words) - 18:11, 11 June 2022
- ==Algebra of generalized functions== |title = Algebra of one-dimensional generalized functions5 KB (730 words) - 07:07, 1 December 2018
- ...ber]] expressed with finite combination of rational numbers and elementary functions.2 KB (368 words) - 18:27, 30 July 2019
- ...roduct, the [[SuperFunction]] of Factorial and that for some other special functions are considered there. ...be the simplest among various SuperFunctions of Factorial, if one exclude functions that are identically equal to a constant.18 KB (2,278 words) - 00:03, 29 February 2024
- [[Category:Abel functions]]3 KB (519 words) - 18:27, 30 July 2019
- The non-integer iteration of function allows to express such functions as Sequently, the Abel functions are also different.4 KB (547 words) - 23:16, 24 August 2020
- [[File:KellerDoyaT.png|300px|thumb|Transfer functions of laser amplifiers with simple kinetics for the short pulses ([[Keller fun H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (11 KB (1,644 words) - 06:33, 20 July 2020
- Most of commonly used functions can be declared as [[transfer function]]s, and the corresponding [[Abel fun ...t/u7327836m2850246/ H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. [[Aequationes Mathematicae]], '''81''', p4 KB (598 words) - 18:26, 30 July 2019
- Functions \(P\) and \(\vec f\!=\!\vec f(x)\) are supposed to be given; \(\nabla\) dif7 KB (1,149 words) - 18:26, 30 July 2019
- where \(u_k\) are assumed to be functions of \(x_1, x_2, x_3\) ; \(k\) and \(j\) and \(i\) take integer values from5 KB (737 words) - 18:26, 30 July 2019
- [[Category:Elementary functions]]4 KB (661 words) - 10:12, 20 July 2020
- ...periods are \(\{2\pi,0,0\}\) and \(\{0,2\pi,0\}\). The velovities \(u\) as functions of coordinates \(x\) are defined as follows: [[Category:Periodic functions]]2 KB (292 words) - 18:26, 30 July 2019
- ...on of the [[Navier-Stokes equation]] can be expressed in term of [[special functions]]. In principle, any function can be declared as "special", if its specific ...t solution of the Navier-Stokes]] refers to the non-trivial combonation of functions \(\vec u=\vec u(\vec x)\) and \(p=p(\vec x)\) such that4 KB (620 words) - 18:25, 30 July 2019
- ...(y=x+\chi\), the derivatives of the transformed field can be espressed as functions of the old coordinates:9 KB (1,358 words) - 18:27, 30 July 2019
- ==Iteration of functions== ...ed, yet, such representation cannot be used even to plot graphics of these functions for non-integer number of iterates.3 KB (438 words) - 18:25, 30 July 2019
- ...functions. JCVI-syn3.0 is a versatile platform for investigating the core functions16 KB (2,012 words) - 01:09, 31 December 2018
- ...refuge in the Russian Federation, handling the privatization of the KGB's functions. In particular, since 1995, Golovatov is president of semi-legal organizati10 KB (848 words) - 15:55, 1 January 2019
- H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. [[Aequationes Mathematicae]], v.81, p.65- ...that grow faster than any polynomial but slower than any exponential. Such functions greatly extend the ability of holomorphic fitting of dependences with non-t7 KB (1,091 words) - 23:03, 30 November 2019
- ...] offers the table of evaluations of some fixed points for some elementary functions [[Category:Mathematical functions]]4 KB (574 words) - 18:26, 30 July 2019
- ...e.math.sfu.ca/~cbm/aands/ Abramowitz and Stegun: Handbook of Mathematical Functions.3 KB (405 words) - 04:09, 1 July 2020
- In [[TORI]], the complex maps are used for illustration many functions, and in particular, those that yet are underrepresented in the literature: [[Category:Mathematical functions]]2 KB (254 words) - 06:59, 1 December 2018
- [[Category:Holomorphic functions]]5 KB (275 words) - 07:00, 1 December 2018
- simplification of mathematical expressions, solving equations, evaluation of functions, plotting graphics and other things that require some [[mathematics]]. ...e coefficients for the approximation for the [[superfunctions]] and [[Abel functions]] using the expansions in vicinity of the [[Fixed point]]s; in particular,12 KB (1,901 words) - 18:43, 30 July 2019
- '''Holomorphic function''' is concept of the theory of functions of complex variables that refers the the existence of the derivative. [[Category:Holomorphic functions]]1 KB (151 words) - 21:08, 25 January 2021
- [[Category:Mathematical functions]] [[Category:Elementary functions]]12 KB (1,754 words) - 18:25, 30 July 2019
- ==Relation to other special functions== According to the Axiom [[TORI]] number 6, the simplest among related functions should be considered as principal, primary. From this axiom, it follows, th27 KB (4,071 words) - 18:29, 16 July 2020
- ==Relation with other functions== [[Category:Holomorphic functions]]8 KB (1,107 words) - 18:26, 30 July 2019
- ...ng with real numbers. However, the difference become clearly seen is these functions are plotted in the complex plane. ...ermined by the two parameters \(P_{\rm sat}\) and \(t\) through the known functions Doya and Tania. Such a model seems to be applied, in particular, for the [[19 KB (2,778 words) - 10:05, 1 May 2021
- After such a header, the functions can be defined as follows: [[Category:Complex(double) functions]]3 KB (480 words) - 14:33, 20 June 2013
- For the integrable continuous functions \(A\) and \(B\), it is assumed that On the set of continuous functions \(A\), the operatot product11 KB (1,501 words) - 18:44, 30 July 2019
- The expression (2) defines the discrete analogy of the simplest [[self-Fourier]] function. With such an input array, The case of the Gaussian self-Fourier function by (2) is shown at the figure at right for \(N\!=\!16\).<br>6 KB (1,010 words) - 13:23, 24 December 2020
- In any pair of holomorphic functions \(F\), \(G\!=\!F^{-1}\), | [[cosinus]], [[trigonometric functions]]11 KB (1,565 words) - 18:26, 30 July 2019
- ...s of the [[SuperFactorial]] and [[AbelFactorial]] (or "ArcSuperFactorial") functions. ...t/u7327836m2850246/ H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. [[Aequationes Mathematicae]], '''81''', p5 KB (750 words) - 18:25, 30 July 2019
- Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188 For iteration of functions, the same notation is used also by [[Walter Bergweiler]]14 KB (2,203 words) - 06:36, 20 July 2020
- 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
