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- ...ffective cross-sections of absorption and emission of light in the physics of [[solid-state laser]]s ...<math>\omega</math>, and let <math>~T~</math> be the effective temperature of the medium. The McCumbner relation is16 KB (2,521 words) - 15:13, 17 June 2020
- ...on]] with fast growth along the real axis; for non-negative integer values of the argument, this function has integer values. <ref name="IRENE"> ....Stegun: Handbook of Mathematical Functions. 6. Gamma Function and Related Functions (2010)27 KB (3,925 words) - 18:26, 30 July 2019
- is the \(\mathbb C \mapsto \mathbb C\) function, which is solution of equations ...n]] of [[exponential]] to base \(b\). Exponential is [[transfer function]] of tetration.21 KB (3,175 words) - 23:37, 2 May 2021
- ...space to itself or to another space, and also the graphical representation of such a function. Such a representation is called '''map'''. ...surface of the Earth (or that of another planet) is mapped to the surface of14 KB (2,275 words) - 18:25, 30 July 2019
- [[Superfunction]] comes from iteration of some function. ...derbrace{T\Big(T\big(... T(t)...\big)\Big)}} \atop {z \mathrm{~evaluations~of~function~}T\!25 KB (3,622 words) - 08:35, 3 May 2021
- [[File:Penplot.jpg|300px|thumb|\(y=\mathrm{pen}(x)\) and related functions.]] [[Natural pentation]] is [[supefrunction]] of [[natural tetration]] tet; [[natural pentation]] satisfies the [[transfer e7 KB (1,090 words) - 18:49, 30 July 2019
- Terras, R. "On the Existence of a Density." Acta Arith. 35, 101-102, 1979. is subsequence of the [[Collatz sequense]]5 KB (798 words) - 18:25, 30 July 2019
- A [[fractional iterate]] $\phi$ of an analytic function $f$ at fixpoint $a$ is called regular, iff $\phi$ is a ...rtrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.20 KB (3,010 words) - 18:11, 11 June 2022
- '''SuperFactorial''', or "superfactorial" is [[superfunction]] of [[factorial]] constructed at its [[fixed point]] 2. Here, the upper index of a function indicates the number of [[iteration]]s.18 KB (2,278 words) - 00:03, 29 February 2024
- [[File:SeregaFunction03.png|600px|thumb|Breaking of the idealized ocean wave]] '''Navier-Stokes equation''' is system of equations for7 KB (1,149 words) - 18:26, 30 July 2019
- ...action]] might be a key to the breakthrough in the efficient approximation of the solutions. The text below uses the ideas by [[Enrico Sciubba]] ...Navier-Stokes equation]], that deduction assumes that the time derivatives of velocities do not vary while velocities do; such an assumption looks incons5 KB (737 words) - 18:26, 30 July 2019
- ...of the [[Noeter theorem]]. Below, the indices that numerate the components of the field and those that numerate the coordinates are recovered. for some Lagrangian \(L=L(x,u(x),u_\bullet(x))\), realizes the extremum of the action9 KB (1,358 words) - 18:27, 30 July 2019
- [[File:Tet5loplot.jpg|400px|thumb|Graphical search for the [[fixed point]]s of [[tetration]]; \(y\!=\!\mathrm{tet}_b(x)\) versus \(x\) for various \(b\) ] For a given function \(f\), the '''fixed point''' is solution \(L\) of equation4 KB (574 words) - 18:26, 30 July 2019
- ...upports this language, developed by the [[Wolfram corporation]] in the end of century 20 for simplification of mathematical expressions, solving equations, evaluation of functions, plotting graphics and other things that require some [[mathematics]].12 KB (1,901 words) - 18:43, 30 July 2019
- At the edges of this range, the Yulya function becomes infinite. The '''ArcYulya function''' is just inverse function of Yulya, id est, \(\mathrm{ArcYulya}_a=\mathrm{Yulya}_a^{-1}\) in such a way,12 KB (1,754 words) - 18:25, 30 July 2019
- ...ion]] (thin curve) to the [[Shoka function]] (thick curve) for real values of the argument]] '''Tania function''' is solution \(f\!=\!\mathrm{Tania}\) of equation27 KB (4,071 words) - 18:29, 16 July 2020
- ...n." From MathWorld--A Wolfram Web Resource. </ref>, is solution \(W=W(z)\) of equations ==Relation with other functions==8 KB (1,107 words) - 18:26, 30 July 2019
- The [[Doya function]] and its iterates appear as the [[transfer function]] of an [[optical amplifier]] with simplest kinetic model. In vicinity of the real axis (While \(|\Im(z)| \!<\! \pi\)), the [[Doya function]] can be19 KB (2,778 words) - 10:05, 1 May 2021
- Let some complex–valued function \(A\) be defined for real values of the argument, id est, ...integral converges, then, function \(B\) is called '''Fourier transform''' of function \(A\).11 KB (1,501 words) - 18:44, 30 July 2019
- ...m''' or '''FFT''', is the efficient algorithm for the numerical evaluation of the [[Discrete Fouler Tansform]] defined with \(A\) is the input array of length \(N\), numbered beginning from 0;<br>6 KB (1,010 words) - 13:23, 24 December 2020