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Results tagged with integral-transforms
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user 49208
For questions about integral transforms, inlcuding the Fourier transform, Laplace transform, Radon transform, Mellin transform, Hankel transform etc.
1
vote
Integral involving exponential and Marcum-Q function
Making a change in the sum $l+k=j$ we immediately evaluate this integral in terms of the Appell hypergeometric function, if the aim was to classify it via something known:
$$
I=\frac{1}{2}\sqrt{\frac{ …
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0
votes
1
answer
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Fourier transform with cubic exponential
Please give references for the integral transform of the next kind:
$$
F_3(f(x))(t)=\int_{-\infty}^{\infty} \exp(Q_3(x,t)) f(t)\,dt ,
$$
with $Q_3(x,t)$ - a cubic polynomial of its arguments. Special …
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2
votes
What function is "$U_{\nu}(\cdot, \cdot)$"?
This is the Lommel function of two variables, cf. p.748 of the book you mentioned for its definition.
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0
votes
Motivating the Bessel translation operator
The generalized translation operator helps to move singularity for PDE from zero to any value.
It helps to define generalized positively defined functions and so on, analogous to use of standard shif …
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2
votes
Accepted
Laplace transform of : $t^{\gamma-1} F(\alpha,\beta,\delta,t)$, where $F$ is the Gauss' hype...
There is an explicit formula in the book:
A.P. Prudnikov, Yu.A. Brychkov, O.I. Marichev. INTEGRALS AND SERIES, Volume 4.
Direct Laplace Transforms. GORDON AND BREACH, 1992.
It is on the page 533 an …
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5
votes
Accepted
Variations on the Mellin and Dirichlet transforms
I know that the discrete Mellin transform was defined by V.S.Ryko:
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=ivm&paperid=5138&option_lang=rus
English reference: Soviet Mathematics (Izv …
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