appelberry
Jun8-10, 05:37 PM
Does anyone know how to prove the following identity:
\Sigma_{k=0}^{n}\left(\stackrel{n}{k}\right) H_{k}(x)H_{n-k}(y)=2^{n/2}H_{n}(2^{-1/2}(x+y))
where H_{i}(z)represents the Hermite polynomial?
\Sigma_{k=0}^{n}\left(\stackrel{n}{k}\right) H_{k}(x)H_{n-k}(y)=2^{n/2}H_{n}(2^{-1/2}(x+y))
where H_{i}(z)represents the Hermite polynomial?