Family of explicitly diagonalizable weighted Hankel matrices generalizing the Hilbert matrix

Pavel Stovicek, Tomas Kalvoda

A three-parameter family $B=B(a,b,c)$ of weighted Hankel matrices is introduced with the entries \[ B_{j,k}=\frac{Γ(j+k+a)}{Γ(j+k+b+c)}\,\sqrt{\frac{Γ(j+b)Γ(j+c)Γ(k+b)Γ(k+c)}{Γ(j+a…