• mathematics, the Mellin transform is an integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform. This integral...
    33 KB (4,679 words) - 18:09, 17 June 2025
  • Thumbnail for Hjalmar Mellin
    is chiefly remembered as the developer of the integral transform known as the Mellin transform. He studied related gamma functions, hypergeometric functions...
    5 KB (385 words) - 04:08, 13 October 2024
  • formula for the inverse Laplace transform, called the Mellin's inverse formula, the Bromwich integral, or the Fourier–Mellin integral, is given by the line...
    8 KB (1,012 words) - 13:27, 30 June 2025
  • Thumbnail for Riemann zeta function
    Retrieved 11 March 2014. Mellin transform and the functional equation of the Riemann Zeta function—Computational examples of Mellin transform methods involving...
    74 KB (10,718 words) - 01:21, 7 July 2025
  • other transforms, most notably the Fourier transform and the Mellin transform. Formally, the Laplace transform is converted into a Fourier transform by the...
    75 KB (9,508 words) - 23:07, 6 July 2025
  • Thumbnail for Riesz function
    The Riesz function is related to the Riemann zeta function via its Mellin transform. If we take M ( R i e s z ( z ) ) = ∫ 0 ∞ R i e s z ( z ) z s d z z...
    9 KB (1,919 words) - 20:31, 29 June 2025
  • _{-T}^{T}x^{\sigma +it}F(\sigma +it)dt.} It is also possible to invert the Mellin transform of the summatory function of f that defines the DGF F of f to obtain...
    25 KB (5,354 words) - 07:02, 13 May 2025
  • mathematics, the Mellin inversion formula (named after Hjalmar Mellin) tells us conditions under which the inverse Mellin transform, or equivalently the...
    5 KB (797 words) - 15:49, 18 July 2024
  • Thumbnail for Fourier transform
    Hankel transform Hartley transform Laplace transform Least-squares spectral analysis Linear canonical transform List of Fourier-related transforms Mellin transform...
    177 KB (21,313 words) - 19:14, 8 July 2025
  • different distributions, then the Mellin transform of their product is equal to the product of their Mellin transforms: M X Y ( s ) = M X ( s ) M Y ( s...
    41 KB (8,987 words) - 08:48, 30 June 2025
  • path integral? Assuming the Abel transform is not discontinuous at u {\displaystyle u} . Some conditions apply, see Mellin inversion theorem for details...
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  • Thumbnail for Divisor summatory function
    \alpha _{k}={\frac {k-1}{2k}}\ .} Both portions may be expressed as Mellin transforms: D ( x ) = 1 2 π i ∫ c − i ∞ c + i ∞ ζ 2 ( w ) x w w d w {\displaystyle...
    11 KB (1,936 words) - 09:00, 30 January 2025
  • Laplace transforms are closely related to the Fourier transform, the Mellin transform, the Z-transform and the ordinary or one-sided Laplace transform. If...
    18 KB (1,995 words) - 01:40, 28 February 2025
  • transforms include: Two-sided Laplace transform Mellin transform, another closely related integral transform Laplace transform: the Fourier transform...
    7 KB (1,001 words) - 15:55, 27 May 2025
  • Salzwedel, in Saxony-Anhalt, Germany. Mellin (surname), surname Mellin transform, in mathematics an integral transform Mellino This disambiguation page lists...
    301 bytes (63 words) - 06:06, 6 October 2024
  • Laplace–Stieltjes transform Legendre transform Associated Legendre transform Linear canonical transform Mellin transform Inverse Mellin transform Poisson–Mellin–Newton...
    3 KB (293 words) - 16:54, 5 July 2025
  • Thumbnail for Ramanujan's master theorem
    Ramanujan, is a technique that provides an analytic expression for the Mellin transform of an analytic function. The result is stated as follows: If a complex-valued...
    29 KB (4,763 words) - 12:54, 1 July 2025
  • Poisson–Mellin–Newton cycle, noted by Flajolet et al. in 1985, is the observation that the resemblance of the Nørlund–Rice integral to the Mellin transform is...
    5 KB (820 words) - 08:26, 1 June 2025
  • the case of Laplace transforms, Mellin transforms will be used specially when solving differential equations. The Mellin transforms of the left-sided and...
    18 KB (2,748 words) - 15:45, 14 May 2025
  • Thumbnail for Fourier analysis
    Fourier-related transforms Laplace transform (LT) Two-sided Laplace transform Mellin transform Non-uniform discrete Fourier transform (NDFT) Quantum Fourier...
    38 KB (4,788 words) - 15:31, 27 April 2025
  • Thumbnail for Meijer G-function
    function. This integral is of the so-called Mellin–Barnes type, and may be viewed as an inverse Mellin transform. The definition holds under the following...
    49 KB (10,023 words) - 12:56, 16 June 2025
  • the Laplace transform, the two-sided Laplace transform and, when suitably modified, for the Mellin transform and Hartley transform (see Mellin inversion...
    22 KB (1,984 words) - 09:41, 9 March 2025
  • Thumbnail for Gamma function
    an entire function. In fact, the gamma function corresponds to the Mellin transform of the negative exponential function: Γ ( z ) = M { e − x } ( z ) ...
    90 KB (13,547 words) - 17:59, 24 June 2025
  • Thumbnail for Dirichlet eta function
    (s)} represents the gamma function). This gives the eta function as a Mellin transform. Hardy gave a simple proof of the functional equation for the eta function...
    19 KB (3,708 words) - 17:02, 5 July 2025
  • transformation Wavelet transform Hankel transform Joukowsky transform Mellin transform Z-transform Keener, James P. 2000. Principles of Applied Mathematics: Transformation...
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  • Thumbnail for Integral
    expansion to determine the integral. The method is closely related to the Mellin transform. Definite integrals may be approximated using several methods of numerical...
    69 KB (9,288 words) - 03:06, 30 June 2025
  • Perron's formula (category Integral transforms)
    calculate the sum of an arithmetic function, by means of an inverse Mellin transform. Let { a ( n ) } {\displaystyle \{a(n)\}} be an arithmetic function...
    3 KB (615 words) - 22:06, 14 November 2024
  • the Euler–Maclaurin summation formula and integral transforms such as the Laplace and Mellin transforms. Repeated integration by parts will often lead to...
    12 KB (1,975 words) - 01:58, 3 June 2025
  • Thumbnail for Mertens conjecture
    integrating by parts, obtain the reciprocal of the zeta function as a Mellin transform 1 s ζ ( s ) = { M M } ( − s ) = ∫ 0 ∞ x − s M ( x ) d x x . {\displaystyle...
    11 KB (1,442 words) - 15:10, 16 January 2025
  • Thumbnail for Convolution
    transform of f {\displaystyle f} . Versions of this theorem also hold for the Laplace transform, two-sided Laplace transform, Z-transform and Mellin transform...
    67 KB (8,819 words) - 22:44, 19 June 2025