1
vote
0answers
70 views

Verification of Fourier transformation of Io-sinh function

I try to match, but it could not match $I_o-\sinh$ Practical Fourier Transform pair developed by Ben Logan, transform pair also published in The Practical Application of the Fourier Integral ...
0
votes
0answers
30 views

integral equation with beta kernel

Is there any way to solve the integral equation $$ z(a,b;x) = 1+\dfrac{(1+x)^{b}}{B(a,b)}\int_0^c\dfrac{y^{a-1}}{(1+x+y)^{a+b}}z(a,b;y)\,dy,\;\;x\ge0, $$ where $a,b,c>0$ are parameters, and ...
0
votes
0answers
37 views

Solution of an integral equation

Consider the integral equation: $$\int_{0}^{\infty}\left(1-\left(\frac{u}{2\pi x} \right )^{1/4}-\exp{\left(\frac{u}{2\pi x} \right )^{1/4}} \right )\eta (x,y)dx=u\delta(u-y)$$ $\delta(\cdot)$ is the ...
4
votes
1answer
292 views

How can I solve this integral equation in terms of Hermite polynomials?

It must be proven that the solution of the integral equation $$f(x)=\int_{-\infty}^{+\infty} e^{-(x-t)^2} g(t)dt$$ is $$g(x)=\frac{1}{\sqrt{}\pi}\sum_{n=0}^{\infty} \frac{f^{(n)}(0)}{2^nn!} H_n(x)$$ ...