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Is there "multiplicative" analogue of Fourier transform?

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#fourier-transform #harmonic-analysis #mellin-transform
205
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Find the inverse of the integral transform $ S_n\{f\}=\int_{0}^1f(x)x^{n}\,dx$

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#real-analysis #complex-analysis #integral-transforms #mellin-transform
109
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Is there a Mellin transform or an analogue on $L^2([0,2\pi])$ or $\ell^2(\mathbb{Z})$?

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#complex-analysis #analysis #fourier-analysis #integral-transforms #mellin-transform
208
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What is the definition of $Li(x)$ in these MathOverflow questions on $I_s =\int_{1}^{\infty} (\pi(x)-Li(x))\,x^{-s-1} dx$?

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#number-theory #prime-numbers #analytic-number-theory #mellin-transform
147
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What is $s\int_1^\infty\sin(2\,\pi\,n\,x)\,x^{-s-1}\,dx$?

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#sequences-and-series #number-theory #riemann-zeta #hypergeometric-function #mellin-transform
207
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Questions on convergence of formula for $\zeta(s)$

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#sequences-and-series #number-theory #riemann-zeta #riemann-hypothesis #mellin-transform
541
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Questions on formulas for the reciprocal gamma function $\frac{1}{\Gamma(s)}$

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#complex-analysis #number-theory #laplace-transform #gamma-function #mellin-transform
322
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Use of Mellin transform for evaluation of a series

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#sequences-and-series #integral-transforms #mellin-transform
45
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Mellin Transform of $h(x-a)$

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#integral-transforms #mellin-transform
94
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An inverse Mellin transform with Gauss hypergeometric function

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#inverse #mellin-transform
148
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Is there a valid explicit formula for $f(x)=\sum\limits_{n=1}^x \frac{1}{n}\sum\limits_{d|n} \mu(d)\,d$?

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#number-theory #riemann-zeta #totient-function #dirichlet-series #mellin-transform
95
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How to get Mellin transform of the given function?

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#real-analysis #integration #improper-integrals #mellin-transform
341
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Asymptotic expansion of the Volterra integral equation with series ansatz

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#complex-analysis #asymptotics #integral-equations #cauchy-integral-formula #mellin-transform
251
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Mellin/Bromwich Integral (Inverse Laplace Transform) problem

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#laplace-transform #mellin-transform #inverse-laplace
125
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How does one invert a p-adic mellin transform, and what does it say about function asymptotics?

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#complex-analysis #harmonic-analysis #p-adic-number-theory #mellin-transform #haar-measure

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