DLMF:18.18.E39 (Q5829)

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DLMF:18.18.E39
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    ∑ ℓ = 0 n ( n ℓ ) ⁢ H ℓ ⁡ ( 2 1 2 ⁢ x ) ⁢ H n - ℓ ⁡ ( 2 1 2 ⁢ y ) = 2 1 2 ⁢ n ⁢ H n ⁡ ( x + y ) , superscript subscript ℓ 0 𝑛 binomial 𝑛 ℓ Hermite-polynomial-H ℓ superscript 2 1 2 𝑥 Hermite-polynomial-H 𝑛 ℓ superscript 2 1 2 𝑦 superscript 2 1 2 𝑛 Hermite-polynomial-H 𝑛 𝑥 𝑦 {\displaystyle{\displaystyle\sum_{\ell=0}^{n}\genfrac{(}{)}{0.0pt}{}{n}{\ell}H% _{\ell}\left(2^{\frac{1}{2}}x\right)H_{n-\ell}\left(2^{\frac{1}{2}}y\right)=2^% {\frac{1}{2}n}H_{n}\left(x+y\right),}}
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    DLMF:18.18.E39
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