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• Factorial
  The cut of range of [[holomorphism]] is shown with black dashed line.
  27 KB (3,925 words) - 18:26, 30 July 2019
• Superfunction
  The modified superfunction may have narrowed range of holomorphism. The narrower is the range of holomorphism, the wider is variety of superfunctions allowed <ref name="walker">
  25 KB (3,622 words) - 08:35, 3 May 2021
• Regular Iteration
  ...iod unity. For the uniqueness, the additional requirements on the range of holomorphism of the [[superfunction]] should be postulated.
  20 KB (3,010 words) - 18:11, 11 June 2022
• SuperFactorial
  ...rivial superfunctions of Factorial show complicated behavior: and even the holomorphism in the left hand side of the complex plane cannot be achieved. Up to year 2
  18 KB (2,278 words) - 00:03, 29 February 2024
• Transfer function
  ...any pair of biholomorphic \(F\) and \(G=F^{-1}\) with wide enough range of holomorphism can be declared as superfunction and Abel function; then \(f(z)=F(1+G(z))\)
  11 KB (1,644 words) - 06:33, 20 July 2020
• ArcTetration
  ..., the conditions of the uniqueness are determined by the requirement of bi-holomorphism in certain range that extends from one fixed point of the exponential to an
  7 KB (1,091 words) - 23:03, 30 November 2019
• LambertW function
  ...f-line along the negative part of the real axis, id est, the domain of the holomorphism is
  8 KB (1,107 words) - 18:26, 30 July 2019
• Square root of exponential
  \(z\mapsto \exp(z)^{1/2}\); in the range of holomorphism, the last can be reduced to \(\exp(z/2)\).
  5 KB (750 words) - 18:25, 30 July 2019
• Natural tetration
  Due to the wide range of holomorphism, and the simple properties, tetration is most important among various [[sup ...of \(\eta(z)\) in the direction of the imaginary axis reduces the range of holomorphism of such a superexponential, destroying its apymptotic approach to \(L\) and
  14 KB (1,972 words) - 02:22, 27 June 2020
• ArcCos
  ==Range of holomorphism==
  5 KB (754 words) - 18:47, 30 July 2019
• ArcSin
  ==Range of holomorphism==
  9 KB (982 words) - 18:48, 30 July 2019
• ArcSinc
  ==Symmetry and holomorphism== The range of holomorphism of \(\mathrm{acosc}(z)\) is the whole complex plane except the cuts
  4 KB (563 words) - 18:27, 30 July 2019

• File:LogQ2mapT2.png The cut of the range of holomorphism is marked with dashed line. Lines $u\!=\!1$, $u\!=\!2$, $u\!=\!4$, $u\!=\!6 (1,765 × 1,729 (1.43 MB)) - 09:43, 21 June 2013

• File:QFactorialQexp.jpg The cuts of the range of [[holomorphic function|holomorphism]] are shown with black dashed lines. (800 × 399 (121 KB)) - 17:23, 11 July 2013

• File:SqrtExpZ.jpg Pink lines indicate the cuts of the range of [[holomorphism]]. (842 × 953 (83 KB)) - 11:56, 21 June 2013

• Интегральная формула Коши
  [[Category:Holomorphism]]
  16 KB (821 words) - 14:42, 21 July 2020
• Julia set
  [[Julia set]], set of values in range of holomorphism of function, but out of holomorphism of some its integer iteration.
  4 KB (630 words) - 18:44, 30 July 2019

• File:Ackerplot.jpg The holomorphism with respect to the argument should be also required. (2,800 × 4,477 (726 KB)) - 08:28, 1 December 2018

• File:Ackerplot400.jpg The holomorphism with respect to the argument should be also required. (3,355 × 4,477 (805 KB)) - 08:29, 1 December 2018

• Ackermann function
  Since 1950, the [[holomorphic function|holomorphism]] had been suggested as the important criterion.
  10 KB (1,534 words) - 06:44, 20 July 2020

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