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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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An integral equation
I have a Fredholm integral equation of second kind
$$\frac{-1}{2\pi \omega'^2}+\int_{-\infty}^{\infty}\frac{1}{\pi \omega'^2}\frac{\psi(\omega)d\omega}{{\text{sinch}}((\omega-\omega')\pi/2)}=\psi(\om …