A family of discrete semi-classical orthogonal polynomials of class one
The paper gives a detailed and complete description of \(D_{\omega}\)-semi-classical sequences \(\{S_n\}_{n\geq 0}\) of class \(s=1\), satisfying the three-term recurrence relation \[ S_{n+2}(x)=(x-(t_n-t_{n+1}))S_{n+1}(x)+t_n^2 S_n(x),\;n\geq 0;\;S_1(x)=x+t_0,\,S_0(x)=1, \] with \(t_n\not= 0,\;n\geq 0\).
scientific article; zbMATH DE number 6865419