DLMF:6.5.E7 (Q2247)

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DLMF:6.5.E7
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    Statements

    Defining formula
    g ⁡ ( z ) ± i ⁢ f ⁡ ( z ) = E 1 ⁡ ( ∓ i ⁢ z ) ⁢ e ∓ i ⁢ z . plus-or-minus sine-cosine-integral-g 𝑧 𝑖 sine-cosine-integral-f 𝑧 exponential-integral minus-or-plus 𝑖 𝑧 superscript 𝑒 minus-or-plus 𝑖 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(z\right)\pm i\mathrm{f}\left(z% \right)=E_{1}\left(\mp iz\right)e^{\mp iz}.}}
    0 references
    DLMF id
    DLMF:6.5.E7
    0 references
    Symbols used
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    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.m2afdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2afdec
    0 references
    auxiliary function for sine and cosine integrals
    Defining formula
    f ⁡ ( z ) sine-cosine-integral-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E17.m2adec
    0 references
    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
    0 references
    Q11305
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1bdec
    0 references
     
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