DLMF:8.5.E4 (Q2513)

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DLMF:8.5.E4
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    Statements

    Defining formula
    γ ⁡ ( a , z ) = a - 1 ⁢ z 1 2 ⁢ a - 1 2 ⁢ e - 1 2 ⁢ z ⁢ M 1 2 ⁢ a - 1 2 , 1 2 ⁢ a ⁡ ( z ) . incomplete-gamma 𝑎 𝑧 superscript 𝑎 1 superscript 𝑧 1 2 𝑎 1 2 superscript 𝑒 1 2 𝑧 Whittaker-confluent-hypergeometric-M 1 2 𝑎 1 2 1 2 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(a,z\right)=a^{-1}z^{\frac{1}{2}a-\frac% {1}{2}}e^{-\frac{1}{2}z}M_{\frac{1}{2}a-\frac{1}{2},\frac{1}{2}a}\left(z\right% ).}}
    0 references
    DLMF id
    DLMF:8.5.E4
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    Symbols used
    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.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
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    incomplete gamma function
    Defining formula
    γ ⁡ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E1.m2aadec
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    Q11323
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1cdec
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    Q11324
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1cdec
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