DLMF:32.11.E18 (Q9453)

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DLMF:32.11.E18
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    Statements

    test
    χ + 3 2 ⁢ d 2 ⁢ ln ⁡ 2 - 1 4 ⁢ π - ph ⁡ Γ ⁡ ( 1 2 ⁢ i ⁢ d 2 ) ≠ n ⁢ π , 𝜒 3 2 superscript 𝑑 2 2 1 4 𝜋 phase Euler-Gamma 1 2 𝑖 superscript 𝑑 2 𝑛 𝜋 {\displaystyle{\displaystyle\chi+\tfrac{3}{2}d^{2}\ln 2-\tfrac{1}{4}\pi-% \operatorname{ph}\Gamma\left(\tfrac{1}{2}id^{2}\right)\neq n\pi,}}
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    DLMF id
    DLMF:32.11.E18
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
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    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2ahdec
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    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1abdec
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    Q12571
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C32.S1.XMD2.m1bdec
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    Q12638
    test
    χ 𝜒 {\displaystyle{\displaystyle\chi}}
    xml-id
    C32.S11.XMD10.m1bdec
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