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Hermite polynomials Chihara starts with the general recurrence relation {$P_{n+1}(x)=[x  (dn + f)]P_n(x)  [n(gn + h)]P_{n1}(x)$} where {$g>0, g+h>0, d, f\in\mathbb{R}$} Hermite polynomials arise when {$d=0, g=0$}. Chihara furthermore sets {$f=0$}. This yields {$P_{n+1}(x)= xP_n(x)  hnP_{n1}(x)$} In my notation {$\alpha=0,\beta=0$} Note that 