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• ArcKeller
  ...e [[Keller function]]; there exist the explicit representations for these functions through the [[elementary function]]s: ...ArcShoka]] and [[Shoka function]]s can be expressed in terms of elementary functions:
  4 KB (545 words) - 18:26, 30 July 2019
• ArcLambertW
  Figure 3 looks pretty similar to the plots of iterates of other functions with fast growth along the real axis.
  3 KB (499 words) - 18:25, 30 July 2019
• SuZex approximation
  ...ed to similar maps for various approximations of [[SuZex]] with elementary functions. All the maps are supposed to be displayed in the same scale.
  14 KB (2,037 words) - 18:25, 30 July 2019
• AuZex
  The should be unique, in order to avoid confusion with other functions, while all figures are collected in the same directory for some article or two different functions are used in the same expression.<br>
  6 KB (899 words) - 18:44, 30 July 2019
• Name of function
  ...in order to distinguish it/him/her from other element of the same set. For functions, the name is especially important because it allows to denote the complicat Usually, the names of functions use the ascii characters, namely, letters and, in exceptional cases, [[cife
  6 KB (901 words) - 18:27, 30 July 2019
• Algebra of Generalized function
  #redirect[[Algebra of generalized functions]]
  45 bytes (5 words) - 14:11, 28 June 2013
• Power function
  These functions can be verified with the Mathematica code below: <poem><nomathjax><nowiki> ...ld be applied to the result. Often this appears dealing with trigonometric functions, one writes, for example, \(\sin^a(z)\) instead of \(\sin(z)^a~\). <!-- How
  15 KB (2,495 words) - 18:43, 30 July 2019
• Trappmann function
  ...in the [[Mathematica]] software, all the names of the implemented special functions begin with capital letter. In this sense, \(\mathrm{Tra}=\mathrm{tra}\). As for the super functions, the capitalisation (for example, \(\mathrm{SuTra}\)) is used to separate t
  9 KB (1,320 words) - 11:38, 20 July 2020
• C++
  In order to follow the descriptions of functions and to reproduce and to modify the figures suggested, the installing of C++ ...enerates the [[contour plot]]s; and in particular, the [[complex map]]s of functions of compex variables
  4 KB (608 words) - 15:01, 20 June 2013
• Schroeder equation
  </ref>; their functions are pretty different.
  8 KB (1,239 words) - 11:32, 20 July 2020
• Fractional iterate
  [[Fractional iterate]] is concept used to construct non-integer iterates of functions.
  2 KB (272 words) - 18:25, 30 July 2019
• Zooming equation
  G. Szekeres. Regular iteration of real and complex functions. </ref>. The non-integer iterates of various functions can be constructed also with the [[superfunction]] and [[Abel function]], c
  10 KB (1,627 words) - 18:26, 30 July 2019
• SuTra
  ...n function is important example of function without [[fixed points]]. Such functions were expected to be difficult for construction of the [[fractional iterate] ==Relation to other special functions==
  9 KB (1,285 words) - 18:25, 30 July 2019
• ArcTra
  ...ing of approximation of solution of algebraic equation with differentiable functions: The agreement functions for the primary approximations app1, app2, app3, app4 described above and f
  10 KB (1,442 words) - 18:47, 30 July 2019
• AuTra
  ...uired to plot the camera-ready pictures of the complex maps of the related functions.
  6 KB (1,009 words) - 18:48, 30 July 2019
• Orwell1984
  ...It was still true that men were not equal in their native talents and that functions had to be specialized in ways that favoured some individuals against others
  587 KB (105,318 words) - 13:23, 7 April 2023
• Abelpower
  These functions are called [[Abelpower]] functions. For \(a\!=\!2\), the explicit plots of these two functions are shown in figure at top.
  3 KB (470 words) - 18:47, 30 July 2019
• Algebra of generalized functions
  [[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
• Nori
  ...tegration. This observation caused the need to perform certain analysis of functions [[mori]], [[nori]], [[naga]] and [[maga]]. ...ant; in particular the efficient implementations are necessary for all the functions involved.
  13 KB (1,759 words) - 18:45, 30 July 2019
• Superlogarithm
  ...ames of routines for elementary functions coincide with the names of these functions.
  1 KB (173 words) - 19:31, 30 July 2019
• 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
• Julia set
  Iteration of meromorphic functions. ...lia]], who had presented the results about invariants of the iteration of functions in 1918
  4 KB (630 words) - 18:44, 30 July 2019
• RAS reform
  ...d be stripped of their property rights, transferring the property managing functions to a federal agency that would be specially created for this purpose.</i> ...d be stripped of their property rights, transferring the property managing functions to a federal agency that would be specially created for this purpose. ..</i
  15 KB (1,750 words) - 18:44, 30 July 2019
• Conjugation
  This applies both to functions and to numbers.
  6 KB (921 words) - 18:46, 30 July 2019
• Mathematical notations
  ...n the operations summation, multiplication, exponentiation and the inverse functions.
  5 KB (753 words) - 18:47, 30 July 2019
• Iterate of exponential
  Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188. Both, tet and ate are holomorphic functions; so, the representation above can be used for non-integer \(n\). The expone
  7 KB (1,161 words) - 18:43, 30 July 2019
• Iterate of linear fraction
  All functions \(P\), \(t^n\) and \(Q\) are defined above, and \(f^n\) is expressed in a w ...nction]] and the [[Abel function]] can be expressed in terms of elementary functions. For many cases, instead of to express the [[superfunction]] through the it
  13 KB (2,088 words) - 06:43, 20 July 2020
• Linear fraction
  ...as usually, the additional conditions on the asymptotic behavior of these functions is required in order to make the non-integer iterate unique.
  5 KB (830 words) - 18:44, 30 July 2019
• Superfunctions
  ...on]]s, [[superfunction]]s, and the non-integer [[iterate]]s of holomorphic functions. Non-integer iterates of holomorphic functions.<br>
  15 KB (2,166 words) - 20:33, 16 July 2023
• Linear fuction
  ...e number \(n\) of iteration has no need to be integer. As other holomophic functions, the linear function can be iterated even complex number of times.
  2 KB (234 words) - 18:43, 30 July 2019
• Freedom
  ...erty of some theory, concept, model, that implies the ability to vary some functions or parameters without to destroy the main properties declared. In some case
  2 KB (355 words) - 10:39, 17 September 2013
• 2014.12.26rubleDollar
  where \(M=209 ~\) is total number of experimental data. Approximating functions are specified below: ...Currency band and the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 838
  5 KB (433 words) - 18:47, 30 July 2019
• Ackermann function
  The first ackermann functions have special names: ...lysis]] are based on the first 3 [[ackermann functions]] and their inverse functions in various combinations.
  10 KB (1,534 words) - 06:44, 20 July 2020
• AdPow
  For \(a\!=\!2\), both functions [[AdPow]] and [[AuPow]] are shown in Fig.1
  2 KB (271 words) - 18:43, 30 July 2019
• Amplitude of oscillator function
  For the asymptotic expansions of various functions with the oscillator function, the asymptotic behaviour of
  6 KB (770 words) - 18:44, 30 July 2019
• Analuxpf3c.cin
  ...] implementation of the elementary function \(\mathrm{Fit}_3\) and related functions, that provides approximation of [[natural tetration]] for moderate values o
  1 KB (253 words) - 18:48, 30 July 2019
• Applied Mathematical Sciences
  ...Currency band and the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 838
  4 KB (610 words) - 06:58, 1 December 2018
• Approximations of ruble
  ...n yen, USA cents and Euro cents, with [[holomorphic function|holomorphic]] functions of time. Various approximations with elementary functions with 3 parameters had been considered. Approximation with ellipses happened
  18 KB (2,080 words) - 13:48, 1 February 2022
• Arcsin.cin
  ...the name of the function here is arcsin, not asin. Comparison of these two functions for 201 real values of the argument can be performed with the routine below
  4 KB (488 words) - 06:58, 1 December 2018
• ArqNem
  The branch points for all inverse functions of the [[Nemtsov function]] \(\mathrm {Nem}_q\) are the same. Four different functions are used dependently on the argument; in order to choose the appropriate al
  7 KB (1,319 words) - 18:46, 30 July 2019
• AuNem
  [[ArqNem]]. It is important to use namely [[ArqNem]], while two other inverse functions, [[ArcNem]] and [[ArkNem]] do not provide the convergence of the iterative ...the special choice of the cut lines of function [[ArqNem]]. Other inverse functions for the [[Nemtsov function]] do not provide this property and, therefore, c
  9 KB (1,441 words) - 18:45, 30 July 2019
• AuPow
  For \(a\!=\!2\), both functions [[AdPow]] and [[AuPow]] are shown in Fig.1
  2 KB (284 words) - 18:43, 30 July 2019
• Base e1e
  ...], [[SuperExponential]] (in particular, the [[tetration]]) and the inverse functions.
  4 KB (559 words) - 17:10, 10 August 2020
• Base sqrt2
  [[Base sqrt2]] is article about functions that refer to base \(b=\sqrt{2}\).
  3 KB (557 words) - 18:46, 30 July 2019
• Chebyshev polynomial
  In [[Mathematica]], the [[Chebyshev polynomial]]s are built-in functions; \(T_n(x)\) is denoted with ChebyshevT[n,x]
  1 KB (186 words) - 18:48, 30 July 2019
• Collapse of RF
  ...[[Vertival of power]] of the [[Fuhrer]] and his [[KGB]] mafia dismount the functions of the state organisations. Even the [[Duma]], Parliament is no anymore pla
  14 KB (1,958 words) - 19:19, 6 August 2022
• Conjecture on superfunctions
  ...ere is at least one approximation of function \(\Phi\) in terms of special functions, that are built-in at the programming languages available for year 2003, ...and the resulting non-integer [[iterate]]s greatly extends the arsenal of functions available for fitting of any physical dependences.
  7 KB (1,031 words) - 03:16, 12 May 2021
• CosFT
  3 KB (468 words) - 18:47, 30 July 2019
• Discrete Bessel
  At the grid, the scalar product of two functions \(\phi\) and \(\psi\) is approximated with Simplest among these functions is Gaussian, \(f(x)=\exp(-x^2/2)\).
  8 KB (1,153 words) - 18:44, 30 July 2019
• Eigendecomposition
  ...lgorithm for dimensions greater than 4 must either be infinite, or involve functions of greater complexity than elementary arithmetic operations and fractional
  4 KB (518 words) - 18:46, 30 July 2019
• Elementary function
  ...ion of the first three [[Ackermann function]]s functions and their inverse functions. The first three ackermann functions are
  3 KB (496 words) - 18:45, 30 July 2019
• Exotic iteration
  ...of regular iteration, while the iterates are regular (id est, holomorphic) functions at least in some vicinity of the fixed point. ...ation''' or '''singular iteration''' could be also used to define the same functions.
  11 KB (1,715 words) - 18:44, 30 July 2019
• Fuhrer
  [[Fuhrer]] ([[Фюрер]]) is the top ruler of a country, who substitutes functions of the state institutions (parliament, senate, ministries, courts, etc.) wi
  6 KB (825 words) - 07:00, 1 December 2018
• Gauss-Laguerre quadrature
  ...efficient in the numerical calculations with approximation of atomic wave functions in spherical coordinates.
  7 KB (997 words) - 18:44, 30 July 2019
• HIKARI Applied Mathematical Sciences
  ...Currency band and the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 838
  3 KB (386 words) - 07:01, 1 December 2018
• Hermite polynomial
  4 KB (628 words) - 18:47, 30 July 2019
• Inverse function
  ==Self-inverse functions== Some functions are their own inverse function.
  3 KB (444 words) - 18:43, 30 July 2019
• Kori
  ...escription and implementation of functions [[kori]] and some other related functions ([[maga]], [[mori]], [[naga]], [[nori]]) appear as [[tool]]s for the descri Several articles about the functions introduced above are expected to be loaded.
  14 KB (1,943 words) - 18:48, 30 July 2019
• LaguerreL
  ...matica]] to denote the [[Laguerre polynomial]] and the associated Laguerre functions.<ref> For each integer non-negative \(k\), the \(k\)th Laguerre functions also form the orthogonal basis at the integration with the exponential wei
  5 KB (759 words) - 18:44, 30 July 2019
• Laplacian in spherical coordinates
  ...he spherical coordinates, their names, and different order of arguments of functions dependent on these coordinates.
  8 KB (1,254 words) - 18:44, 30 July 2019
• Linear approximation
  In application of mathematical analysis, all functions are known with some finite precision, and the first approximation may negle
  4 KB (670 words) - 18:46, 30 July 2019
• Lof
  ...aginary part of the argument, it is, indeed, just combination of these two functions. ...some critics for introducing new name for so simple combination of special functions, [[Logarithm]] and [[Factorial]]; both of them are implemented, for example
  3 KB (478 words) - 18:43, 30 July 2019
• Maga
  ...jpg|300px|thumb|\(y\!=\!\mathrm{maga}(x)\) (thick black curve) and related functions]] ...the complex plane. For the last option, the holomorphic properties of the functions involved (and their complex maps) should be analysed.
  8 KB (1,256 words) - 18:44, 30 July 2019
• Morinaga function
  ...the performance, the contour integral may be considered. However, all the functions in the integrand should be implemented for the complex values of the argume
  15 KB (2,303 words) - 18:47, 30 July 2019
• Naga
  ...simple combination of the [[Bessel function]] [[BesselJ0]] with elementary functions: ==Relation with other functions==
  5 KB (750 words) - 10:00, 20 July 2020
• NemBra
  while two other its inverse functions [[ArcNem]] and [[ArkNem]] gives the unnecessary cut lines of the [[Abel fun
  4 KB (618 words) - 18:46, 30 July 2019
• NemBran
  Functions [[SuNem]] and [[AuNem]] are used to express the non-integer iterates of the On the most of applications, the only real–values functions are used.
  3 KB (400 words) - 18:48, 30 July 2019
• Nembran.cin
  ...e [[Nemtsov function]]. The same is also branch point of two other inverse functions of the [[Nemtsov Finction]], [[ArcNem]] and [[ArkNem]], but namely [[ArqNem
  2 KB (281 words) - 07:03, 1 December 2018
• Nemtsov function
  ...e Nemtsov function are considered, and also some properties of the related functions: ...versions had been assigned (designated) the different names. These inverse functions have different positions of the cuts of the range of holomorphism.
  14 KB (2,157 words) - 18:44, 30 July 2019
• Nyquist theorem
  ...the real axis, through the linear combination of equidistantly–displaced functions [[sinc]]: ...s of the Fourier representaion. It refers to the [[Fourier transform]]s of functions \(f\) and \(u\):
  6 KB (944 words) - 18:48, 30 July 2019
• Orthogonal polynomials
  [[Orthogonal polynomials]] is specific set of orthogonal functions, used, in particular, for construction of formulas of [[numerical integrati
  6 KB (918 words) - 18:47, 30 July 2019
• Oscillator function
  ...gative \(n\), the solution \(F_n\) can be expressed in terms of elementary functions, in comparison to the oscillator functions \)F\(.
  6 KB (846 words) - 18:47, 30 July 2019
• Pentation
  The additional condition, common for all ackermann functions is assumed,
  5 KB (803 words) - 18:48, 30 July 2019
• Plodi.cin
  ...used to draw maps of agreement, that characterizes difference between two functions.
  1 KB (207 words) - 07:04, 1 December 2018
• Pluralism
  H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (
  6 KB (950 words) - 18:48, 30 July 2019
• Radial equation for hydrogen atom
  The radial wave functions are orthogonal;
  8 KB (1,199 words) - 18:45, 30 July 2019
• SdPow
  ...xpressed as elementary functions. For \(a\!=\!2\), these functions are who functions are shown in Fig.1.
  1 KB (202 words) - 18:48, 30 July 2019
• Sergey Melnik
  Memory Functions of the Additive Markov Chains: Applications to Complex Dynamic Systems. Memory functions and Correlations in Additive Binary Markov Chains.
  9 KB (670 words) - 07:05, 1 December 2018
• Series
  ...essel function]]; attempts to reproduce similar inconsistencies with other functions are not successful.
  2 KB (325 words) - 18:44, 30 July 2019
• Sin
  The postulating of some properties of some functions may have sense while no proof is available. Properties of functions [[sin]] and [[cos]], can be deduced from the differential equation above. A
  4 KB (680 words) - 18:43, 30 July 2019
• SinFT
  5 KB (807 words) - 18:44, 30 July 2019
• Special function
  ...lation of the function to other elementary functions or with other special functions, defined earlier; even if the relation is asymptotic or approximate. ...valent of one dollar''' would be suitable in their descriptions as special functions.
  7 KB (991 words) - 18:48, 30 July 2019
• SuNem
  ...mplification of he algorithm, the precision and speed of evaluation of the functions are expected to improve a little bit. With functions [[SuNem]] and [[AuNem]], the iterates of the Nemtsov function can be writte
  6 KB (967 words) - 18:44, 30 July 2019
• SuPow
  The period \(P=2\pi\mathrm i / \ln(a)\) is the same for both these functions. Functions [[SuPow]] and [[SdPow]] are related with expression
  3 KB (405 words) - 18:43, 30 July 2019
• SuSin
  ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188</ref>. SuSin can be aproximated with elementary functions.
  15 KB (2,314 words) - 18:48, 30 July 2019
• Thermal diffusion of Gaussian
  ...al variables \(x\). Parameters \(\alpha\) and \(\beta\) are supposed to be functions of time. Evolution of these parameters can be determined from the thermal d
  4 KB (554 words) - 18:43, 30 July 2019
• Trigonometry
  [[Trigonometry]] means set of tools to handle with combinations of functions [[sin]] and [[cos]], and also, the skills to use these tools. Some formulas
  453 bytes (59 words) - 18:43, 30 July 2019
• Инфляция
  ...Currency band and the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 838
  38 KB (636 words) - 18:37, 30 July 2019
• Нет Путина - нет России
  ...Currency band and the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 838
  44 KB (813 words) - 13:37, 14 April 2023
• Taylor-Green vortex
  ...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 (291 words) - 18:27, 30 July 2019
• Фальшивомонетничество
  ...Currency band and the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 838.
  14 KB (164 words) - 18:46, 30 July 2019
• 2018.03.04.Теракт
  ...toxic chemicals that stop the nervous system working and shut down bodily functions. // ...toxic chemicals that stop the nervous system working and shut down bodily functions. //
  153 KB (3,732 words) - 23:19, 30 December 2019
• Alien in a foreign sea 1
  ...ance. The organism was fighting the opposite way - suddenly including some functions, so that its owner was in a situation that makes clear the thoughts about d
  367 KB (65,743 words) - 15:48, 1 February 2019
• ArcNem
  [[ArcNem]] is one of inverse functions of the [[Nemtsov function]], For positive values \(x\) of the argument, these four functions coincide:
  6 KB (1,099 words) - 18:46, 30 July 2019
• ArkNem
  [[ArcNem]] is one of inverse functions of the [[Nemtsov function]], For positive values \(x\) of the argument, these four functions coincide:
  3 KB (524 words) - 18:47, 30 July 2019
• FullSimplify
  ...s a wide range of transformations on expr involving elementary and special functions and returns the simplest form it finds.<br>
  2 KB (305 words) - 18:43, 30 July 2019
• Meganesia.Deportation
  ...amily gathered on the central terrace<!--, to perform the custom of living functions!-->. However, Irji was already sitting at the computer and doing something ...usual motive for participation in tenders for the execution of government functions.»
  143 KB (24,042 words) - 12:47, 3 April 2021
• Nemtsov function and its iterates
  G. Szekeres. Regular iteration of real and complex functions. Acta Mathematica, September 1958, Volume 100, Issue 3, pp 203-258. W.Bergweiler. Iteration of meromorphic functions. Bulletin (New Series) of the American Mathematical society, v.29, No.2 (19
  15 KB (2,392 words) - 11:05, 20 July 2020
• Банда наркоманов
  ...toxic chemicals that stop the nervous system working and shut down bodily functions. //
  133 KB (3,747 words) - 09:56, 28 April 2022
• Модель коллапсирующей экономики
  ...Currency band and the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 838 //
  39 KB (760 words) - 11:55, 22 April 2023

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