DLMF:13.20.E5 (Q4594)

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DLMF:13.20.E5
No description defined

    Statements

    Defining formula
    W κ , μ ⁡ ( x ) = x X ⁢ ( 2 ⁢ μ 2 - κ ⁢ x + μ ⁢ X ( μ - κ ) ⁢ x ) μ ⁢ ( X + x - 2 ⁢ κ 2 ) κ ⁢ e - 1 2 ⁢ X - κ ⁢ ( 1 + O ⁡ ( 1 μ ) ) , Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑥 𝑥 𝑋 superscript 2 superscript 𝜇 2 𝜅 𝑥 𝜇 𝑋 𝜇 𝜅 𝑥 𝜇 superscript 𝑋 𝑥 2 𝜅 2 𝜅 superscript 𝑒 1 2 𝑋 𝜅 1 Big-O 1 𝜇 {\displaystyle{\displaystyle W_{\kappa,\mu}\left(x\right)=\sqrt{\frac{x}{X}}\*% \left(\frac{2\mu^{2}-\kappa x+\mu X}{(\mu-\kappa)x}\right)^{\mu}\*\left(\frac{% X+x-2\kappa}{2}\right)^{\kappa}\*e^{-\frac{1}{2}X-\kappa}\*\left(1+O\left(% \frac{1}{\mu}\right)\right),}}
    0 references
    DLMF id
    DLMF:13.20.E5
    0 references
    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
    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.m2aadec
    0 references
    Q11566
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C13.S1.XMD4.m1cdec
    0 references
    DLMF:13.20.E3
    Defining formula
    X 𝑋 {\displaystyle{\displaystyle X}}
    xml-id
    C13.S20.XMD1.m1bdec
    0 references
    DLMF:13.20.E3
    Defining formula
    X 𝑋 {\displaystyle{\displaystyle X}}
    xml-id
    C13.S20.XMD1.m1bdec
    0 references
     
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