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  • ...the real parameter \(\varepsilon\) such that at \(\varepsilon\!=\!0\), the transform is identical, id est, \(y\!=\!x\) and \(v\!=\!u\); and in the linear approx ...variation takes place inside some domain \(x\in \Omega\); assume \(O\) is transform on \(\Omega\).
    9 KB (1,358 words) - 18:27, 30 July 2019
  • '''Fourier transform''' is linear integral transform with the exponential [[kernel]]. If the integral converges, then, function \(B\) is called '''Fourier transform''' of function \(A\).
    11 KB (1,501 words) - 18:44, 30 July 2019
  • '''Fourier-2 transform''' is bidimensional [[Fourier transform]] The transform \(g\) of a function \(f\) is defined with expression
    6 KB (954 words) - 18:27, 30 July 2019
  • '''Bessel Transform''' or BesselTransform, called also '''Hankel transform''' ==Hankel transform and Bessel transform==
    8 KB (1,183 words) - 10:21, 20 July 2020
  • '''Discrete Hankel transform''' is the numerical analogy of the [[Bessel transform]]. http://www.gnu.org/software/gsl/manual/html_node/Discrete-Hankel-Transform-Definition.html</ref> is copypasted with minimal torification.
    7 KB (1,063 words) - 18:25, 30 July 2019
  • ==Integral representations== ...s can be used for testing of the numerical implementations of the [[Bessel transform]].
    13 KB (1,592 words) - 18:25, 30 July 2019
  • '''CosFourier''' or '''CosTransform''' is [[integral operator]] with kernel defined on the set of functions \(f\) such that the integral below converges:
    6 KB (915 words) - 18:26, 30 July 2019
  • ...length in a way, that have some analogies with the integral [[CosFourier]] transform There are many kinds of the DiscreteCos transform, and many corresponding algorithms are implemented. Usually, they are poorl
    3 KB (482 words) - 18:26, 30 July 2019
  • [[DCTI]] is one of realizations of the [[Discrete Cos transform]] operator. Numerical Recipes in C. Fast Sine and Cosine transform.
    10 KB (1,447 words) - 18:27, 30 July 2019
  • [[DCT]] may refer to the '''Discrete cosine transform'''. The four kinds of DCT are often in use; Gilbert Strang. The Discrete Cosine Transform. SIAM REVIEW (Copyright 1999 by Society for Industrial and Applied Mathemat
    10 KB (1,689 words) - 18:26, 30 July 2019
  • ...r (Discrete Cosine transform); it is one of many discrete analogies of the integral operator [[CosFourier]]. Numerilal implementation of the transform DCTII consists of 3 files: [[zfour1.cin]], [[zrealft.cin]], [[zcosft2.cin]]
    5 KB (682 words) - 18:27, 30 July 2019
  • (integral, where the integrand is expressed only in terms of already known, id est, s If deal with a differential equation with partial derivatives, and some transform allows to express the solution in terms of an ordinary differential equatio
    2 KB (351 words) - 15:00, 20 June 2013
  • ...r (Discrete Cosine transform); it is one of many discrete analogies of the integral operator [[CosFourier]]. ...only antisimmetric modes can be performed with the [[DST]] (Discrete sine transform).
    6 KB (825 words) - 18:25, 30 July 2019
  • ...d to the cases of other fixed points \(~L~\), performing the corresponding transform of the transfer function from \(~T~\) to \(~t~\), ...by Helmuth Kneser in 1950, and in 2011, the solution through the [[Cauchi integral]] and the [[superfunction]] had been suggested.
    10 KB (1,627 words) - 18:26, 30 July 2019
  • [[CFT]], is the discrete implementation of the [[CosFT]] transform. ...e of CFT routine, that reproduces, up to the rounding errors, the identity transform of the array in the First column, \(~\)CFT(CFT(\(f\)))\(\,\approx f~\).
    5 KB (721 words) - 18:44, 30 July 2019
  • [[CosFT]], or Cosinus Transform, refers to the integral transform with kernel \(K(x,y)=\sqrt{\frac{2}{\pi}} \cos(xy)\); the sine transform [[SinFT]] of function \(f\) appears as \(g=\,\)[[SinFT]]\(f\) with rofmula
    3 KB (468 words) - 18:47, 30 July 2019
  • ...chanics and integral transform of a functions (see, for example, [[Fourier transform]]).
    3 KB (444 words) - 18:43, 30 July 2019
  • ...performed in a straightforward way), or search for the appropriate contour integral in the complex plane. For the last option, the holomorphic properties of th Integral in the definition of function[[Maga]] can be expressed through the Fourier
    8 KB (1,256 words) - 18:44, 30 July 2019
  • Morinaga function appears at the [[Bessel transform]] of the principal Bessel mode ...converted to the momentum representation, this mode leads to the [[Bessel transform]]
    15 KB (2,303 words) - 18:47, 30 July 2019
  • ...on the inigueness of the Fourier representaion. It refers to the [[Fourier transform]]s of functions \(f\) and \(u\): Now I substitute representation of \(f\) through its Fourier transform \(F\), this gives
    6 KB (944 words) - 18:48, 30 July 2019

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