DLMF:13.18.E16 (Q4585)

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DLMF:13.18.E16
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    Statements

    Defining formula
    W 1 4 + 1 2 ⁢ n , 1 4 ⁡ ( z 2 ) = 2 - n ⁢ e - 1 2 ⁢ z 2 ⁢ z ⁢ H n ⁡ ( z ) . Whittaker-confluent-hypergeometric-W 1 4 1 2 𝑛 1 4 superscript 𝑧 2 superscript 2 𝑛 superscript 𝑒 1 2 superscript 𝑧 2 𝑧 Hermite-polynomial-H 𝑛 𝑧 {\displaystyle{\displaystyle W_{\frac{1}{4}+\frac{1}{2}n,\frac{1}{4}}\left(z^{% 2}\right)=2^{-n}e^{-\frac{1}{2}z^{2}}\sqrt{z}H_{n}\left(z\right).}}
    0 references
    DLMF id
    DLMF:13.18.E16
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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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    Whittaker confluent hypergeometric function
    Defining formula
    W κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E3.m2afdec
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