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- ...the character appear at the top or at the bottom of the screen while some mathematical text is displayed. However, sometimes, the range of definition of a charact ...[[theorem]], and remain undefined outside. In this sense, the structure of mathematical texts is similar to the structure of some [[algorithmic languages]], such a8 KB (1,403 words) - 14:24, 20 June 2013
- ....Stegun: Handbook of Mathematical Functions. 6. Gamma Function and Related Functions (2010) The American Mathematical Monthly, Vol. 103, No. 3 (Mar., 1996), pp. 214-220, http://www.jstor.org/p27 KB (3,925 words) - 18:26, 30 July 2019
- D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45. H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (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
- D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45. H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (14 KB (2,275 words) - 18:25, 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.]] ...adie.pdf D.Kouznetsov. Superexponential as special function. [[Vladikavkaz Mathematical Journal]], 2010, v.12, issue 2, p.31-45.7 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 ( D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.13 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
- [[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
- ...y]] (Moscow) in 1948. Worked in the same university, then in the [[Steklov Mathematical Institute]] (Moscow). He wrote more than 100 scientific papers ==Algebra of generalized functions==5 KB (730 words) - 07:07, 1 December 2018
- and is denoted with symbol \(\ln\) in [[mathematical notations]]; ...number larger than unity. If the base is not \(\mathrm e\), then in the [[mathematical notations]] the symbol "log" is used; the base is indicated as subscript:4 KB (661 words) - 10:12, 20 July 2020
- ==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
- H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. [[Aequationes Mathematicae]], v.81, p.65- D.Kouznetsov. Superexponential as special function. [[Vladikavkaz Mathematical Journal]], 2010, v.12, issue 2, p.31-45.7 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
- :[[Mathematical statistics]] ...lgorithms. There exist special programming languages for simplification of mathematical deduction; the most popular are [[Mathematica]] and [[Maple (software)|Mapl3 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
- 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
- [[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
- ...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
- 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 XINZHI LIU. Stability of Impulsive Control Systems with Time Delay. Mathematical and Computer Modelling 39 (2004) 511-519.14 KB (2,203 words) - 06:36, 20 July 2020
- 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
- ...is important), in analogy with property [[periodicity]] of functions in [[mathematical analysis]]. Each periodic process can be interpreted as [[clock]], id set,3 KB (464 words) - 14:33, 20 June 2013
- ...ed presentation and hard discussion of the superfunctions and the transfer functions of laser amplifiers (uniqueness of the superfunction, the range of applicab ...ion to the Jerome Moloney group (University of Arizona, Arizona center for mathematical science).8 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 ( ...vladie.pdf D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.6 KB (312 words) - 18:33, 30 July 2019
- Applied Mathematical Sciences, Vol. 4, 2010, no. 21, p.1021-1032. Keith B.Oldham, Jerome Spainer. The fractional calculus. Mathematical science and engineering, Vol. 111, Academic Press 1974.9 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 ( ...vladie.pdf D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.7 KB (381 words) - 18:38, 30 July 2019
- //Other functions defined below provide approximations for various parts of the complex plane ...vladie.pdf D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.9 KB (654 words) - 07:00, 1 December 2018
- Four mathematical constants are defined above. In order to avoid confusions with single–let Knowledge of these constants simplifies evaluation of functions [[ArcCosc]] and [[ArcCohc]].8 KB (1,137 words) - 18:27, 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
- 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
- While no mathematical proof of uniqueness is available, it should be assumed that the function wi ...quence and its inverse functions can be expressed in terms of [[elementary functions]],7 KB (886 words) - 18:26, 30 July 2019
- Bulletin of the Americal Mathematical Society, v. 65, p.89-93 (1959). For this reason, both functions, [[Tania function]] and [[WrightOmega]] are used in [[TORI]].4 KB (610 words) - 10:22, 20 July 2020
- ...letters (and sometimes, also [[numerical digit]]s) used to identify the [[mathematical function]]s. ...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 complicat6 KB (901 words) - 18:27, 30 July 2019
- ...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 t9 KB (1,320 words) - 11:38, 20 July 2020
- 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]], c10 KB (1,627 words) - 18:26, 30 July 2019
- Applied Mathematical Sciences, Vol. 7, 2013, no. 131, 6527 - 6541 ...n function is important example of function without [[fixed points]]. Such functions were expected to be difficult for construction of the [[fractional iterate]9 KB (1,285 words) - 18:25, 30 July 2019
- ...t and intricate that you could lose yourself in them as in the depths of a mathematical problem — delicate pieces of forgery in which you had nothing to guide yo ...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 others587 KB (105,318 words) - 13:23, 7 April 2023
- [[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
- ...justed parameters. (Here, \(M_2\) is not an adjusting parameter, but exact mathematical constant). Similar goal can be formulated for the numerical implementation ...tegration. This observation caused the need to perform certain analysis of functions [[mori]], [[nori]], [[naga]] and [[maga]].13 KB (1,759 words) - 18:45, 30 July 2019
- 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
- ...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. ..</i15 KB (1,750 words) - 18:44, 30 July 2019
- [[Conjugation]] is certain type of transformation of mathematical objects. This applies both to functions and to numbers.6 KB (921 words) - 18:46, 30 July 2019
- ...to describe the theoretical values of a physical quantity. In this manner, mathematical notation serves as a common language for expressing ideas and results acros ...ers e and <math>\pi</math>, etvetera. Such names form the basics of the '''mathematical notations'''.5 KB (753 words) - 18:47, 30 July 2019
- 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 expone7 KB (1,161 words) - 18:43, 30 July 2019
- 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 it13 KB (2,088 words) - 06:43, 20 July 2020
- ...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
- where \(M=209 ~\) is total number of experimental data. Approximating functions are specified below: ...the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 8385 KB (433 words) - 18:47, 30 July 2019
- 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
- Term [[Applied Mathematical Sciences]] may refer to one of the two following [[scientific journal]]s: [[HIKARI Applied Mathematical Sciences]] http://www.m-hikari.com/ams/4 KB (610 words) - 06:58, 1 December 2018
- ...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 happened18 KB (2,080 words) - 13:48, 1 February 2022
- D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45. D.Kouznetsov. Entire function with logarithmic asymptotic. Applied Mathematical Sciences, 2013, v.7, No.131, p.6527-6541.7 KB (1,031 words) - 03:16, 12 May 2021
- ...ion of the first three [[Ackermann function]]s functions and their inverse functions. The first three ackermann functions are3 KB (496 words) - 18:45, 30 July 2019
- [[HIKARI Applied Mathematical Sciences]] is scientific journal, APPLIED MATHEMATICAL SCIENCES.3 KB (386 words) - 07:01, 1 December 2018
- ...he spherical coordinates, their names, and different order of arguments of functions dependent on these coordinates. ...quantity should not be confused with integer parameter \(\ell\), nor with mathematical constant8 KB (1,254 words) - 18:44, 30 July 2019
- In application of mathematical analysis, all functions are known with some finite precision, and the first approximation may negle4 KB (670 words) - 18:46, 30 July 2019
- The additional condition, common for all ackermann functions is assumed, ...vladie.pdf D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.5 KB (803 words) - 18:48, 30 July 2019
- 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. A4 KB (680 words) - 18:43, 30 July 2019
- [[Special function]] is any mathematical function, supplied with the following: ...lation of the function to other elementary functions or with other special functions, defined earlier; even if the relation is asymptotic or approximate.7 KB (991 words) - 18:48, 30 July 2019
- ...ydns.jp/PAPERS/2014susin.pdf D.Kouznetsov. Super sin. Far East Journal of Mathematical Science, v.85, No.2, 2014, pages 219-238. ...-4/S0273-0979-1993-00432-4.pdf Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188</ref>.15 KB (2,314 words) - 18:48, 30 July 2019
- ...the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 83838 KB (636 words) - 18:37, 30 July 2019
- ...the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 83844 KB (813 words) - 13:37, 14 April 2023
- ...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
- ...mpiled so that it is convenient to disassemble. True, you need to know the mathematical economy, but it runs in parallel, this is part of mathematics. ...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 d367 KB (65,743 words) - 15:48, 1 February 2019
- G. Szekeres. Regular iteration of real and complex functions. Acta Mathematica, September 1958, Volume 100, Issue 3, pp 203-258. Journal of Mathematical Analysis and Applications,15 KB (2,392 words) - 11:05, 20 July 2020
- ...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
- ...the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 83816 KB (266 words) - 17:36, 7 February 2019
- ...the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 838 ...the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 83819 KB (242 words) - 19:05, 7 January 2021
- ...ehavior of solution of the [[Transfer equation]] with exponential transfer functions. The quantities mentioned are plotted in Fig.1 as functions of \(\beta\)4 KB (548 words) - 14:27, 12 August 2020
- ...the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 838 ...the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 83822 KB (367 words) - 18:07, 7 January 2021
- ...als happen to be not sufficient for the numerical analysis of mathematical functions. at the [[fixed point]] 4. Only in the strip along the real axis, these functions look similar.10 KB (1,491 words) - 18:09, 11 June 2022
- ...the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 83829 KB (652 words) - 23:45, 16 July 2022
- ...the approximations: Fitting of rouble with 3-parametric functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 83838 KB (802 words) - 02:21, 25 August 2022
- Fitting of Rouble with 3-Parametric Functions. Applied Mathematical Sciences, Vol. 9, 2015, no. 17, 831 - 838 HIKARI Ltd, www.m-hikari.com http39 KB (759 words) - 16:14, 9 April 2024
