DLMF:6.4.E7 (Q2240)

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DLMF:6.4.E7
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    Statements

    Defining formula
    g ⁡ ( z ⁢ e ± π ⁢ i ) = ∓ π ⁢ i ⁢ e ∓ i ⁢ z + g ⁡ ( z ) . sine-cosine-integral-g 𝑧 superscript 𝑒 plus-or-minus 𝜋 𝑖 minus-or-plus 𝜋 𝑖 superscript 𝑒 minus-or-plus 𝑖 𝑧 sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(ze^{\pm\pi i}\right)=\mp\pi ie^{% \mp iz}+\mathrm{g}\left(z\right).}}
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    DLMF id
    DLMF:6.4.E7
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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.m2aedec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aedec
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    auxiliary function for sine and cosine integrals
    Defining formula
    g ⁡ ( z ) sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E18.m2adec
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