DLMF:6.5.E1 (Q2241)

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DLMF:6.5.E1
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    Statements

    test
    E 1 ⁡ ( - x ± i ⁢ 0 ) = - Ei ⁡ ( x ) ∓ i ⁢ π , exponential-integral plus-or-minus 𝑥 𝑖 0 minus-or-plus exponential-integral-Ei 𝑥 𝑖 𝜋 {\displaystyle{\displaystyle E_{1}\left(-x\pm i0\right)=-\mathrm{Ei}\left(x% \right)\mp i\pi,}}
    0 references
    DLMF id
    DLMF:6.5.E1
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    exponential integral
    test
    E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E1.m2adec
    0 references
    Q11306
    test
    Ei ⁡ ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}
    xml-id
    C6.S2.SS1.p3.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    Q11307
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C6.S1.XMD1.m1dec
    0 references
     
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