DLMF:13.14.E21 (Q4510)

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DLMF:13.14.E21
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    Statements

    Defining formula
    W κ , μ ⁡ ( z ) ∼ e - 1 2 ⁢ z ⁢ z κ , asymptotically-equals Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜅 {\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)\sim e^{-\frac{1}{2}z% }z^{\kappa},}}
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    DLMF id
    DLMF:13.14.E21
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    constraint
    | ph ⁡ z | ≤ 3 2 ⁢ π - δ phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle\left|\operatorname{ph}z\right|\leq\frac{3}{2}\pi-% \delta}}
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    Symbols used
    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.m2akdec
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    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2aadec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2amdec
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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1aadec
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