# Questions tagged [integral-transforms]

For questions about integral transforms, inlcuding the Fourier transform, Laplace transform, Radon transform, Mellin transform, Hankel transform etc.

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### Inversion of integral transforms

We have the following theorem statement of this Paper "An inversion formula for a Class of integral transforms, 1975, C.Nasim" page 8. Let $\phi(x)= \frac{1}{x} \int_{0}^{x} \psi(t) dt$, ...
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### Integral with 4 Bessel functions and an exponential

I would like to solve the following integral $$\int_0^\infty e^{-a k^2} J_{3/2}(b k) J_{3/2}(c k) J_{3/2}(f k) J_{1/2}(r k) k^{-3} dk,$$ where $a,b,c,f,r > 0$, and $J_\nu(x)$ is the Bessel ...
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### Uniqueness of the inverse kernel of an invertible integral transform

For any invertible integral transform $T$ of kernel $K$ that maps a function $f$ to the function $\varphi$ such that $$\varphi(s)=\left[T\left\lbrace f\right\rbrace\right](s)=\int_a^bK(x,s)f(x)dx$$ ...