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DLMF:13.14.E3 - MaRDI portal

DLMF:13.14.E3 (Q5189)

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DLMF:13.14.E3
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    Statements

    DLMF defining formula
    W κ , μ ⁡ ( z ) = e - 1 2 ⁢ z ⁢ z 1 2 + μ ⁢ U ⁡ ( 1 2 + μ - κ , 1 + 2 ⁢ μ , z ) , Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 superscript 𝑒 1 2 𝑧 superscript 𝑧 1 2 𝜇 Kummer-confluent-hypergeometric-U 1 2 𝜇 𝜅 1 2 𝜇 𝑧 {\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=e^{-\frac{1}{2}z}z^{% \frac{1}{2}+\mu}U\left(\tfrac{1}{2}+\mu-\kappa,1+2\mu,z\right),}}
    0 references
    Symbols used
    Kummer confluent hypergeometric function
    DLMF 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.m2adec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1bdec
    0 references
     
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