DLMF:13.2.E6 (Q4296)

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DLMF:13.2.E6
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    Statements

    Defining formula
    U ⁡ ( a , b , z ) ∼ z - a , asymptotically-equals Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑧 𝑎 {\displaystyle{\displaystyle U\left(a,b,z\right)\sim z^{-a},}}
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    DLMF id
    DLMF:13.2.E6
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    constraint
    | ph ⁡ z | ≤ 3 2 ⁢ π - δ phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\frac{3}{2}\pi-\delta}}
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    z → ∞ → 𝑧 {\displaystyle{\displaystyle z\to\infty}}
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    | ph ⁡ z | ≤ 3 2 ⁢ π - δ ph 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\frac{3}{2}\pi-\delta}}
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    Symbols used
    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2adec
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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.m2adec
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