DLMF:18.9.E26 (Q5622)

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DLMF:18.9.E26
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    Statements

    Defining formula
    d d x ⁡ ( e - x 2 ⁢ H n ⁡ ( x ) ) = - e - x 2 ⁢ H n + 1 ⁡ ( x ) . derivative 𝑥 superscript 𝑒 superscript 𝑥 2 Hermite-polynomial-H 𝑛 𝑥 superscript 𝑒 superscript 𝑥 2 Hermite-polynomial-H 𝑛 1 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}x}\left(e^{-x^{2}}H_{n% }\left(x\right)\right)=-e^{-x^{2}}H_{n+1}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.9.E26
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    Symbols used
    Q10922
    Defining formula
    H n ⁡ ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r13.m2abdec
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    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2akdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1zdec
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