DLMF:13.14.E17 (Q4506)

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DLMF:13.14.E17
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    Statements

    Defining formula
    W κ , 1 2 ⁡ ( z ) = 1 Γ ⁡ ( 1 - κ ) + O ⁡ ( z ⁢ ln ⁡ z ) , Whittaker-confluent-hypergeometric-W 𝜅 1 2 𝑧 1 Euler-Gamma 1 𝜅 Big-O 𝑧 𝑧 {\displaystyle{\displaystyle W_{\kappa,\frac{1}{2}}\left(z\right)=\frac{1}{% \Gamma\left(1-\kappa\right)}+O\left(z\ln z\right),}}
    0 references
    DLMF id
    DLMF:13.14.E17
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    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2acdec
    0 references
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aedec
    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.m2ahdec
    0 references
     
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