Results 211 to 220 of about 16,055 (246)

The Mellin Transform

2002
In this and the next chapter, we study the Mellin transform, which, while closely related to the Fourier transform, has its own peculiar uses. In particular, it turns out to be a most convenient tool for deriving asymptotic expansions, although it has other applications ...
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The mellin-whittaker integral transform [PDF]

Mathematical Notes of the Academy of Sciences of the USSR, 1986
The author gives an inversion formula for the integral transform \(\iint K(\xi,\eta,\alpha,\beta,\lambda)f(\xi,\eta,\lambda)d\xi d\eta =F(\alpha,\beta,\lambda)\) with the kernel \[ K=\{(2\lambda)^{2i\alpha +1}B(i(\alpha +\beta)+1/2,i(\alpha -\beta)+1/2)/_{2\Gamma (2i\alpha +1)}\}\cdot \] \[ \eta^{2i}e^{\beta \pi sign \xi \eta -i\lambda \xi \eta}\Phi (i(
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On an integral transform of the Mellin type

Journal of Engineering Mathematics, 1980
This paper establishes an inversion formula for an integral transform of the Mellin type which is defined on a truncated infinite interval ...
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Residue Integrals and their Mellin Transforms

Canadian Journal of Mathematics, 1995
AbstractGiven an almost arbitrary holomorphic map we study the structure of the associated residue integral and its Mellin transform, and the relation between these two objects. More precisely, we relate the limit behaviour of the residue integral to the polar structure of the Mellin transform.
A. K. Tsikh, Mikael Passare
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On the Mellin transforms of hypergeometric polynomials

Journal of Physics A: Mathematical and General, 1999
The authors discuss Mellin integral transform pairs for hypergeometric orthogonal polynomials from the Askey scheme, namely the classical Hermite polynomials, the Laguerre and the Charlier polynomials, the Jacobi and the Meixner polynomials, the continuous Hahn and the dual Hahn polynomials, and the Wilson and the four-parameter Racah polynomials.
Natig M. Atakishiyev, M. K. Atakishiyeva
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Additional Mellin Transforms

2009
This table contains Mellin transforms to supplement the ones at the end of Chap. 1. These are still a small fraction of the transforms that are listed in Marichev (1983). The special functions that are not commonly used are defined in Appendix B. The value of n is an integer in the transforms below.
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The Mellin-wavelet transform

1995 International Conference on Acoustics, Speech, and Signal Processing, 2002
Most machine speech analysis and processing is based on a warped spectral representation. The intent of the paper is to present a method by which proper warped representations can be computed efficiently. In the case of log-warping functions, the methods of the paper produce a wavelet-like transform as a linear convolution of a single log-warped ...
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Eine schnelle Mellin-Transformation

Computing, 1984
A numerical method is developed which handles the Mellin transform (1) \(M_{\epsilon}(y;f)=\int^{\infty}_{0}x^{-iy-\epsilon}f(x)dx,y\in [0,\infty),\epsilon \geq 0,i=\sqrt{\quad -1}\) of a Fourier-bandlimited function f(x). Denoting \(F(z)(F(z)=0\) for \(z\geq Z_ 0)\) the Fourier transform of the even continuation of f(x), then instead of (1) one can ...
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From AdS to dS exchanges: Spectral representation, Mellin amplitudes, and crossing

Physical Review D, 2021
Charlotte Sleight, Massimo Taronna
exaly  

Bootstrapping inflationary correlators in Mellin space

Journal of High Energy Physics, 2020
Charlotte Sleight, Massimo Taronna
exaly