DLMF:13.14.E2 (Q4491)

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DLMF:13.14.E2
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    Statements

    Defining formula
    M κ , μ ⁡ ( z ) = e - 1 2 ⁢ z ⁢ z 1 2 + μ ⁢ M ⁡ ( 1 2 + μ - κ , 1 + 2 ⁢ μ , z ) , Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 superscript 𝑒 1 2 𝑧 superscript 𝑧 1 2 𝜇 Kummer-confluent-hypergeometric-M 1 2 𝜇 𝜅 1 2 𝜇 𝑧 {\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=e^{-\frac{1}{2}z}z^{% \frac{1}{2}+\mu}M\left(\tfrac{1}{2}+\mu-\kappa,1+2\mu,z\right),}}
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    DLMF id
    DLMF:13.14.E2
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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.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1adec
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