DLMF:13.14.E5 (Q4494)

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DLMF:13.14.E5
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    Statements

    Defining formula
    U ⁡ ( a , b , z ) = e 1 2 ⁢ z ⁢ z - 1 2 ⁢ b ⁢ W 1 2 ⁢ b - a , 1 2 ⁢ b - 1 2 ⁡ ( z ) . Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑒 1 2 𝑧 superscript 𝑧 1 2 𝑏 Whittaker-confluent-hypergeometric-W 1 2 𝑏 𝑎 1 2 𝑏 1 2 𝑧 {\displaystyle{\displaystyle U\left(a,b,z\right)=e^{\frac{1}{2}z}z^{-\frac{1}{% 2}b}W_{\frac{1}{2}b-a,\frac{1}{2}b-\frac{1}{2}}\left(z\right).}}
    0 references
    DLMF id
    DLMF:13.14.E5
    0 references
    Symbols used
    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.m2aadec
    0 references
    Whittaker confluent hypergeometric function
    Defining formula
    W κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E3.m2aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1ddec
    0 references
     
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