DLMF:13.14.E4 (Q4493)

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DLMF:13.14.E4
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    Statements

    Defining formula
    M ⁡ ( a , b , z ) = e 1 2 ⁢ z ⁢ z - 1 2 ⁢ b ⁢ M 1 2 ⁢ b - a , 1 2 ⁢ b - 1 2 ⁡ ( z ) , Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 superscript 𝑒 1 2 𝑧 superscript 𝑧 1 2 𝑏 Whittaker-confluent-hypergeometric-M 1 2 𝑏 𝑎 1 2 𝑏 1 2 𝑧 {\displaystyle{\displaystyle M\left(a,b,z\right)=e^{\frac{1}{2}z}z^{-\frac{1}{% 2}b}M_{\frac{1}{2}b-a,\frac{1}{2}b-\frac{1}{2}}\left(z\right),}}
    0 references
    DLMF id
    DLMF:13.14.E4
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    Symbols used
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ 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.m2aadec
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    Whittaker confluent hypergeometric function
    Defining formula
    M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E2.m2aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1cdec
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    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1cdec
    0 references
     
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