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Results tagged with numerical-integration
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user 99045
3
votes
Accepted
Gaps between roots of consecutive Hermite polynomials
The answers are yes and yes.
Consider the Hermite Gauss functions : $\psi_n(x)=e^{-x^2/2}H_n(x) $, we have two properties:
$$\psi_n''(x)+(2n+1-x^2)\psi_n(x)=0 $$
and
$$\psi_{n+1}=\psi_n'(x) +x\psi_n …
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