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Hermite polynomials

Chihara starts with the general recurrence relation

{$P_{n+1}(x)=[x - (dn + f)]P_n(x) - [n(gn + h)]P_{n-1}(x)$} 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

{$P_{n+1}(x)= xP_n(x) - hnP_{n-1}(x)$}

In my notation


Note that

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This page was last changed on January 11, 2024, at 07:15 PM