Integral transforms | Complex analysis | Laplace transforms

Mellin transform

In mathematics, the Mellin transform is an integral 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 Dirichlet series, and isoften used in number theory, mathematical statistics, and the theory of asymptotic expansions; it is closely related to the Laplace transform and the Fourier transform, and the theory of the gamma function and allied special functions. The Mellin transform of a function f is The inverse transform is The notation implies this is a line integral taken over a vertical line in the complex plane, whose real part c need only satisfy a mild lower bound. Conditions under which this inversion is valid are given in the Mellin inversion theorem. The transform is named after the Finnish mathematician Hjalmar Mellin, who introduced it in a paper published 1897 in Acta Societatis Scientiarum Fennicæ. (Wikipedia).

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From playlist ELECTRICAL ENGINEERING 18: THE FOURIER TRANSFORM

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Bangalore Area String Meeting URL: http://www.icts.res.in/discussion_meeting/BASM2016/ DATES: Monday 25 Jul, 2016 - Wednesday 27 Jul, 2016 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore DESCRIPTION: This meeting is designed to bring together string theorists working in the Bangalore

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Related pages

Line integral | Multiplicative group | Locally compact abelian group | Plancherel theorem | Bessel function | Prime-counting function | Scale invariance | Big O notation | Asymptotic expansion | Laplace transform | Parseval's theorem | Mathematical statistics | Meromorphic function | Ramanujan's master theorem | Mellin inversion theorem | Gamma function | Mathematics | Principal branch | Dirac delta function | Generalized normal distribution | Integral transform | Riemann zeta function | Riesz mean | Two-sided Laplace transform | Isometry | Number theory | Harmonic oscillator | Zeros and poles | Haar measure | Hilbert space | Binomial transform | Lp space | Heaviside step function | Perron's formula | Dirichlet series | Fourier transform | Digital Library of Mathematical Functions