DLMF:18.18.E13 (Q5803)

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DLMF:18.18.E13
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    H n ( λ x ) = λ n = 0 n / 2 ( - n ) 2 ! ( 1 - λ - 2 ) H n - 2 ( x ) . Hermite-polynomial-H 𝑛 𝜆 𝑥 superscript 𝜆 𝑛 superscript subscript 0 𝑛 2 Pochhammer 𝑛 2 superscript 1 superscript 𝜆 2 Hermite-polynomial-H 𝑛 2 𝑥 {\displaystyle{\displaystyle H_{n}\left(\lambda x\right)=\lambda^{n}\sum_{\ell% =0}^{\left\lfloor n/2\right\rfloor}\frac{{\left(-n\right)_{2\ell}}}{\ell!}(1-% \lambda^{-2})^{\ell}H_{n-2\ell}\left(x\right).}}
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