DLMF:18.17.E35 (Q5776)

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DLMF:18.17.E35
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    Defining formula
    ∫ - ∞ ∞ e - x ⁢ z ⁢ H n ⁡ ( x ) ⁢ e - x 2 ⁢ d x = π 1 2 ⁢ ( - z ) n ⁢ e 1 4 ⁢ z 2 , superscript subscript superscript 𝑒 𝑥 𝑧 Hermite-polynomial-H 𝑛 𝑥 superscript 𝑒 superscript 𝑥 2 𝑥 superscript 𝜋 1 2 superscript 𝑧 𝑛 superscript 𝑒 1 4 superscript 𝑧 2 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}e^{-xz}H_{n}\left(x\right)e% ^{-x^{2}}\mathrm{d}x=\pi^{\frac{1}{2}}(-z)^{n}e^{\frac{1}{4}z^{2}},}}
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    DLMF id
    DLMF:18.17.E35
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