DLMF:13.6.E18 (Q4405)

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DLMF:13.6.E18
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    Statements

    Defining formula
    U ⁡ ( 1 2 - 1 2 ⁢ n , 3 2 , z 2 ) = 2 - n ⁢ z - 1 ⁢ H n ⁡ ( z ) . Kummer-confluent-hypergeometric-U 1 2 1 2 𝑛 3 2 superscript 𝑧 2 superscript 2 𝑛 superscript 𝑧 1 Hermite-polynomial-H 𝑛 𝑧 {\displaystyle{\displaystyle U\left(\tfrac{1}{2}-\tfrac{1}{2}n,\tfrac{3}{2},z^% {2}\right)=2^{-n}z^{-1}H_{n}\left(z\right).}}
    0 references
    DLMF id
    DLMF:13.6.E18
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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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    Kummer confluent hypergeometric function
    Defining formula
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2ahdec
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    Q11559
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1bdec
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    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1qdec
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