DLMF:15.12.E1 (Q5161)

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DLMF:15.12.E1
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    Statements

    test
    α ± = arctan ⁡ ( ph ⁡ z - ph ⁡ ( 1 - z ) ∓ π ln ⁡ | 1 - z - 1 | ) , subscript 𝛼 plus-or-minus minus-or-plus phase 𝑧 phase 1 𝑧 𝜋 1 superscript 𝑧 1 {\displaystyle{\displaystyle\alpha_{\pm}=\operatorname{arctan}\left(\frac{% \operatorname{ph}z-\operatorname{ph}\left(1-z\right)\mp\pi}{\ln|1-z^{-1}|}% \right),}}
    0 references
    DLMF id
    DLMF:15.12.E1
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    Q10816
    test
    arctan ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m7adec
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    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
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    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
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    Q11644
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1dec
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    Q11680
    test
    α ± subscript 𝛼 plus-or-minus {\displaystyle{\displaystyle\alpha_{\pm}}}
    xml-id
    C15.S12.XMD1.m1dec
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