DLMF:6.5.E6 (Q2246)

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DLMF:6.5.E6
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    Statements

    Defining formula
    Ci ⁡ ( z ) = - 1 2 ⁢ ( E 1 ⁡ ( i ⁢ z ) + E 1 ⁡ ( - i ⁢ z ) ) , cosine-integral 𝑧 1 2 exponential-integral 𝑖 𝑧 exponential-integral 𝑖 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(z\right)=-\tfrac{1}{2}(E_{1}\left% (iz\right)+E_{1}\left(-iz\right)),}}
    0 references
    DLMF id
    DLMF:6.5.E6
    0 references
    Symbols used
    cosine integral
    Defining formula
    Ci ⁡ ( z ) cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E11.m2aadec
    0 references
    exponential integral
    Defining formula
    E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E1.m2aedec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aedec
    0 references
    Q11305
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1adec
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