DLMF:6.4.E5 (Q2238)

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DLMF:6.4.E5
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    Statements

    Defining formula
    Chi ⁡ ( z ⁢ e ± π ⁢ i ) = ± π ⁢ i + Chi ⁡ ( z ) , hyperbolic-cosine-integral 𝑧 superscript 𝑒 plus-or-minus 𝜋 𝑖 plus-or-minus 𝜋 𝑖 hyperbolic-cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Chi}\left(ze^{\pm\pi i}\right)=\pm\pi i+% \mathrm{Chi}\left(z\right),}}
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    DLMF id
    DLMF:6.4.E5
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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.m2acdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
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    hyperbolic cosine integral
    Defining formula
    Chi ⁡ ( z ) hyperbolic-cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Chi}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E16.m2adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
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    Q11305
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1ddec
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