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• BesselJ1
  The [[complex map]] of \(f=J_1(x+\mathrm i y)\) is shown at right in the \(x,y\) plane wi ...an be used to plot the complex map at least for \(z<10\) withe the complex(double) arithmetics is available. For large values of \(|z|\), the asymptotic expa
  3 KB (439 words) - 18:26, 30 July 2019
• Discrete Fourier
  ...etimes the special font is used to avoid the confusion with parameters and functions.) #include <complex>
  6 KB (1,032 words) - 18:48, 30 July 2019
• DCTI
  ...he application in wave optics, '''z_type''' should be defined as [[complex(double)]]; however, for other applications, such a type may be defined in other wa The name of the functions and sense of the arguments are chosen following notations by the [[Numerica
  10 KB (1,447 words) - 18:27, 30 July 2019
• DCT
  ...denote the set of [[real number]]s; however, the same formulas remain for complex numbers and for quaternions, and for many other objects that can be multipl ...he application in wave optics, '''z_type''' should be defined as [[complex(double)]]; however, for other applications, such a type may be defined in other wa
  10 KB (1,689 words) - 18:26, 30 July 2019
• LogisticSequence
  where \(z\) is complex number and \(s\) is real number; usually it is assumed that \(s>1\). ...plots of LogisticSequence are shown in two figures at right. Below, the [[complex map]]s of function \(\mathrm{LogisticSequence}_s\) are shown for \(s\!=\!3\
  7 KB (886 words) - 18:26, 30 July 2019
• SuZex approximation
  [[File:SuZexMapT.jpg|600px|thumb|Fig.2.[[Complex map]] of function [[SuZex]]: \(~u\!+\!\mathrm i v= \mathrm{SuZex}(x_1+x\!+\ ...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
• Power function
  These functions can be verified with the Mathematica code below: <poem><nomathjax><nowiki> [[Complex map]] of the quadratic function (\(a\!=\!2\)) is shown in figure 2 at right
  15 KB (2,495 words) - 18:43, 30 July 2019
• SuTra
  ...\ln(-z)\) at large \(z\) for the most of \(\arg(z)\), id set, in the whole complex plane except the strip along the real axis This is close to the limit that can be achieved with the complex(double) variables.
  9 KB (1,285 words) - 18:25, 30 July 2019
• ArcTra
  Together, the expansions above cover with primary approximations all the complex plane \(z=z+\mathrm i y\) except two halflines ...ing of approximation of solution of algebraic equation with differentiable functions:
  10 KB (1,442 words) - 18:47, 30 July 2019
• AuTra
  are directed to the left hand side of the complex plane, parallel to the real axis. In [[TORI]], this is default choice of th This section describe the [[complex double]] numerical implementation of AuTra. For \(M=9\), the figure at right show
  6 KB (1,009 words) - 18:48, 30 July 2019
• Orwell1984
  ...y there were fear, hatred, and pain, but no dignity of emotion, no deep or complex sorrows. All this he seemed to see in the large eyes of his mother and his ...not readily talk about their jobs. In the long, windowless hall, with its double row of cubicles and its endless rustle of papers and hum of voices murmurin
  587 KB (105,318 words) - 13:23, 7 April 2023
• Nori
  Complex map of function nori is shown at rites with levels \(u=\mathrm{const}\) and if evaluated with complex double variables, the first 24 terms of this expansion provide of order of 15 corr
  13 KB (1,759 words) - 18:45, 30 July 2019
• Iterate of exponential
  Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188. ...ve can be used for non-integer \(n\). The exponential can be iterated even complex number of times.
  7 KB (1,161 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 ...os]]. In general, function [[Amos]]=[[amos]] can be treated as function of complex argument. For real values of the argument, this function and its asymptotic
  6 KB (770 words) - 18:44, 30 July 2019
• Arcsin.cin
  ...mplex double]] routine in [[C++]] for evaluation of function [[ArcSin]] of complex argument. ...ome reason, the compiler recognises [[exp]], [[log]], [[sin]], [[cos]], of complex argument, but fails with asin and acos.
  4 KB (488 words) - 06:58, 1 December 2018
• AuNem
  For \(q\!=\!0\), \(q\!=\!1\) and \(q\!=\!2\), [[complex map]] of function \(\mathrm{AuNem}_q\) is shown in figures 2,3,4. ==Extension to the whole complex plane==
  9 KB (1,441 words) - 18:45, 30 July 2019
• CosFT
  ...ould be replaced to something appropriate, for example, double, or complex double.
  3 KB (468 words) - 18:47, 30 July 2019
• Kori
  Explicit plot and [[complex map]] of function [[kori]] are shown in figures at right. Kori is [[entire function]], it is holomorphic in the whole complex plane. The zero in the denominator in the definition is compensated with th
  14 KB (1,943 words) - 18:48, 30 July 2019
• Morinaga function
  Below, the [[complex map]] of the [[Morinaga function]] is compared to that of function [[Bessel ...imit the range of applicability of this expansion. With double (or complex double) variables, with \(M\!=\!16\) , while last term with coefficient \(c_{15}\)
  15 KB (2,303 words) - 18:47, 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 #include <complex>
  2 KB (281 words) - 07:03, 1 December 2018

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