DLMF:13.6.E17 (Q4404)

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DLMF:13.6.E17
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    Statements

    Defining formula
    M ⁡ ( - n , 3 2 , z 2 ) = ( - 1 ) n ⁢ n ! ( 2 ⁢ n + 1 ) ! ⁢ 2 ⁢ z ⁢ H 2 ⁢ n + 1 ⁡ ( z ) , Kummer-confluent-hypergeometric-M 𝑛 3 2 superscript 𝑧 2 superscript 1 𝑛 𝑛 2 𝑛 1 2 𝑧 Hermite-polynomial-H 2 𝑛 1 𝑧 {\displaystyle{\displaystyle M\left(-n,\tfrac{3}{2},z^{2}\right)=(-1)^{n}\frac% {n!}{(2n+1)!2z}H_{2n+1}\left(z\right),}}
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    DLMF id
    DLMF:13.6.E17
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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.m2aadec
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    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
    Defining formula
    M ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E2.m2aidec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
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