Logan's problem for Jacobi transform

D. V. Gorbachev, V. I. Ivanov, S. Yu. Tikhonov

We consider direct and inverse Jacobi transforms with measures $d\mu (t)=2^{2\rho }(\sinh t{)}^{2\alpha +1}(\cosh t{)}^{2\beta +1}dt$ and $dσ(λ)=(2π)^{-1}\bigl|\frac{2^{ρ-iλ}Γ(α+1)Γ(iλ)} {Γ((ρ+iλ)/2)Γ…