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• McCumber relation
  ...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 is
  16 KB (2,521 words) - 15:13, 17 June 2020
• Factorial
  ...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
• Tetration
  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
• Mapping
  ...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 of
  14 KB (2,275 words) - 18:25, 30 July 2019
• Superfunction
  [[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
• Natural pentation
  [[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 e
  7 KB (1,090 words) - 18:49, 30 July 2019
• Holomorphic extension of the Collatz subsequence
  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
• Regular Iteration
  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
  '''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
• Navier-Stokes equation
  [[File:SeregaFunction03.png|600px|thumb|Breaking of the idealized ocean wave]] '''Navier-Stokes equation''' is system of equations for
  7 KB (1,149 words) - 18:26, 30 July 2019
• Navier-Stokes from variational principle
  ...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 incons
  5 KB (737 words) - 18:26, 30 July 2019
• Proof:Noeter theorem
  ...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 action
  9 KB (1,358 words) - 18:27, 30 July 2019
• Fixed point
  [[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 equation
  4 KB (574 words) - 18:26, 30 July 2019
• Mathematica
  ...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
• Yulya function
  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
• Tania function
  ...ion]] (thin curve) to the [[Shoka function]] (thick curve) for real values of the argument]] '''Tania function''' is solution \(f\!=\!\mathrm{Tania}\) of equation
  27 KB (4,071 words) - 18:29, 16 July 2020
• LambertW function
  ...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
• Doya function
  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 be
  19 KB (2,778 words) - 10:05, 1 May 2021
• Fourier transform
  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
• FFT
  ...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

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