DLMF:6.4.E4 (Q2237)

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DLMF:6.4.E4
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    Statements

    Defining formula
    Ci ⁡ ( z ⁢ e ± π ⁢ i ) = ± π ⁢ i + Ci ⁡ ( z ) , cosine-integral 𝑧 superscript 𝑒 plus-or-minus 𝜋 𝑖 plus-or-minus 𝜋 𝑖 cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(ze^{\pm\pi i}\right)=\pm\pi i+% \mathrm{Ci}\left(z\right),}}
    0 references
    DLMF id
    DLMF:6.4.E4
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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.m2abdec
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    cosine integral
    Defining formula
    Ci ⁡ ( z ) cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E11.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q11305
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1cdec
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