DLMF:23.18.E6 (Q7366)

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DLMF:23.18.E6
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    Statements

    Defining formula
    ε ⁢ ( 𝒜 ) = exp ⁡ ( π ⁢ i ⁢ ( a + d 12 ⁢ c + s ⁢ ( - d , c ) ) ) , 𝜀 𝒜 𝜋 𝑖 𝑎 𝑑 12 𝑐 𝑠 𝑑 𝑐 {\displaystyle{\displaystyle\varepsilon(\mathcal{A})=\exp\left(\pi i\left(% \frac{a+d}{12c}+s(-d,c)\right)\right),}}
    0 references
    DLMF id
    DLMF:23.18.E6
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    Symbols used
    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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    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
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    Q12084
    Defining formula
    𝒜 𝒜 {\displaystyle{\displaystyle\mathcal{A}}}
    xml-id
    C23.S15.XMD1.m1cdec
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    Q12085
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C23.S15.XMD2.m1dec
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    Q12087
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C23.S15.XMD4.m1adec
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    Q12088
    Defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C23.S15.XMD5.m1adec
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    Q12092
    Defining formula
    ε ⁢ ( 𝒜 ) 𝜀 𝒜 {\displaystyle{\displaystyle\varepsilon(\mathcal{A})}}
    xml-id
    C23.S18.XMD3.m1adec
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