• convolution into multiplication. Once solved, the inverse Laplace transform reverts to the original domain. The Laplace transform is defined (for suitable functions...
    75 KB (9,508 words) - 23:07, 6 July 2025
  • In mathematics, the inverse Laplace transform of a function F {\displaystyle F} is a real function f {\displaystyle f} that is piecewise-continuous,...
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  • In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean space...
    20 KB (3,344 words) - 15:39, 29 May 2025
  • Z-transform (redirect from Z-transformation)
    {\displaystyle {\bigg .}X^{*}(s)=X(z){\bigg |}_{\displaystyle z=e^{sT}}} The inverse Laplace transform is a mathematical abstraction known as an impulse-sampled...
    43 KB (5,636 words) - 18:49, 7 June 2025
  • centered at p deviates from f (p). The Laplace operator is named after the French mathematician Pierre-Simon de Laplace (1749–1827), who first applied the...
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  • In classical mechanics, the Laplace–Runge–Lenz vector (LRL vector) is a vector used chiefly to describe the shape and orientation of the orbit of one...
    79 KB (10,218 words) - 19:44, 20 May 2025
  • satisfying ad − bc ≠ 0. Geometrically, a Möbius transformation can be obtained by first applying the inverse stereographic projection from the plane to the...
    70 KB (10,603 words) - 19:06, 8 June 2025
  • Thumbnail for Fourier transform
    −⁠a/2π⁠. This theorem implies the Mellin inversion formula for the Laplace transformation, f ( t ) = 1 i 2 π ∫ b − i ∞ b + i ∞ F ( s ) e s t d s {\displaystyle...
    177 KB (21,313 words) - 02:40, 6 July 2025
  • transform that may be regarded as the multiplicative version of the two-sided Laplace transform. This integral transform is closely connected to the theory of...
    33 KB (4,679 words) - 18:09, 17 June 2025
  • fractional Fourier, Laplace, Gauss–Weierstrass, Bargmann and the Fresnel transforms as particular cases. The name "linear canonical transformation" is from canonical...
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  • Thumbnail for Spherical harmonics
    }^{m}({\mathbf {r} })} , are known as Laplace's spherical harmonics, as they were first introduced by Pierre Simon de Laplace in 1782. These functions form an...
    75 KB (12,488 words) - 15:48, 6 July 2025
  • diagonal, and the inverse of the matrix of eigenvectors. This is called the eigendecomposition and it is a similarity transformation. Such a matrix A is...
    102 KB (13,621 words) - 15:09, 12 June 2025
  • physical linearized pressure coefficient is then obtained by the inverse transformation C p = − 2 ϕ x V ∞ = − 2 β 2 ϕ ¯ x ¯ V ∞ = 1 β 2 C ¯ p {\displaystyle...
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  • Thumbnail for Convolution
    operation ( f ∗ g ) ( t ) {\displaystyle (f*g)(t)} can be defined as the inverse Laplace transform of the product of F ( s ) {\displaystyle F(s)} and G ( s...
    67 KB (8,819 words) - 22:44, 19 June 2025
  • first integral formula corresponds to the Laplace transform (or sometimes the formal Laplace–Borel transformation) of generating functions, denoted by L...
    62 KB (11,140 words) - 06:58, 19 March 2025
  • {\displaystyle g^{\mu \nu }} denotes the inverse of the metric tensor. The Hodge Laplacian, also known as the Laplacede Rham operator, is a differential operator...
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  • Thumbnail for Chi-squared distribution
    the binomial, normal, and chi-squared distributions, as follows. De Moivre and Laplace established that a binomial distribution could be approximated by...
    45 KB (6,817 words) - 10:25, 19 March 2025
  • 319, S2CID 123637858 Laplace, Pierre-Simon, de (1772), "Recherches sur le calcul intégral et sur le systéme du monde", Histoire de l'Académie Royale des...
    91 KB (14,395 words) - 21:11, 31 May 2025
  • Thumbnail for Inverse Gaussian distribution
    inverse Gaussian distribution are provided for the R programming language by several packages including rmutil, SuppDists, STAR, invGauss, LaplacesDemon...
    28 KB (3,168 words) - 15:15, 25 May 2025
  • Glossary of engineering: A–L (category CS1 German-language sources (de))
    transformer used in three-phase power systems. De Moivre–Laplace theorem In probability theory, the de Moivre–Laplace theorem, which is a special case of the...
    279 KB (31,747 words) - 15:19, 3 July 2025
  • Thumbnail for Normal distribution
    ISBN 978-0-19-852341-3. Laplace, Pierre-Simon de (1774). "Mémoire sur la probabilité des causes par les événements". Mémoires de l'Académie Royale des Sciences de Paris...
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  • Thumbnail for Logarithm
    1000 = 3. As a single-variable function, the logarithm to base b is the inverse of exponentiation with base b. The logarithm base 10 is called the decimal...
    98 KB (11,674 words) - 13:55, 4 July 2025
  • inference, which used uniform priors following Laplace's principle of insufficient reason, was called "inverse probability" (because it infers backwards from...
    33 KB (3,425 words) - 13:44, 13 April 2025
  • Thumbnail for Matrix (mathematics)
    provides a method to calculate the determinant of any matrix. Finally, the Laplace expansion expresses the determinant in terms of minors, that is, determinants...
    128 KB (15,715 words) - 23:44, 6 July 2025
  • Thumbnail for Siméon Denis Poisson
    to the Bureau des Longitudes succeeding Pierre-Simon Laplace in 1827. In 1817, he married Nancy de Bardi and with her, he had four children. His father...
    35 KB (4,498 words) - 02:20, 26 May 2025
  • Thumbnail for Partial differential equation
    formula" of the Laplace equation. This is in striking contrast to the case of ordinary differential equations (ODEs) roughly similar to the Laplace equation...
    49 KB (6,800 words) - 08:09, 10 June 2025
  • including by demonstrating that the Laplace–Runge–Lenz vector is constant, or by applying a duality transformation to a 2-dimensional harmonic oscillator...
    128 KB (16,223 words) - 22:06, 30 June 2025
  • Thumbnail for Gaussian integral
    Gauss published the precise integral in 1809, attributing its discovery to Laplace. The integral has a wide range of applications. For example, with a slight...
    21 KB (4,365 words) - 06:30, 29 May 2025
  • Hermite transform (category CS1 German-language sources (de))
    f_{H}(n)=\int _{-\infty }^{\infty }e^{-x^{2}}\ H_{n}(x)\ F(x)\ dx} The inverse Hermite transform H − 1 { f H ( n ) } {\displaystyle H^{-1}\{f_{H}(n)\}}...
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  • inference, which used uniform priors following Laplace's principle of insufficient reason, was called "inverse probability" (because it infers backwards from...
    62 KB (7,600 words) - 04:41, 25 May 2025