DLMF:13.20.E2 (Q4591)

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DLMF:13.20.E2
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    Statements

    Defining formula
    W κ , μ ⁡ ( x ) = π - 1 2 ⁢ Γ ⁡ ( κ + μ ) ⁢ ( 1 4 ⁢ x ) 1 2 - μ ⁢ ( 1 + O ⁡ ( μ - 1 ) ) , Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑥 superscript 𝜋 1 2 Euler-Gamma 𝜅 𝜇 superscript 1 4 𝑥 1 2 𝜇 1 Big-O superscript 𝜇 1 {\displaystyle{\displaystyle W_{\kappa,\mu}\left(x\right)=\pi^{-\frac{1}{2}}% \Gamma\left(\kappa+\mu\right)\left(\tfrac{1}{4}x\right)^{\frac{1}{2}-\mu}\left% (1+O\left(\mu^{-1}\right)\right),}}
    0 references
    DLMF id
    DLMF:13.20.E2
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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.m2aadec
    0 references
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
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    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.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
     
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