DLMF:6.2.E8 (Q2218)

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DLMF:6.2.E8
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    Statements

    test
    li ⁡ ( x ) = ⨍ 0 x d t ln ⁡ t = Ei ⁡ ( ln ⁡ x ) , logarithmic-integral 𝑥 superscript subscript principal-value-integral 0 𝑥 𝑡 𝑡 exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{li}\left(x\right)=\pvint_{0}^{x}\frac{% \mathrm{d}t}{\ln t}=\mathrm{Ei}\left(\ln x\right),}}
    0 references
    DLMF id
    DLMF:6.2.E8
    0 references
    constraint
    x > 1 𝑥 1 {\displaystyle{\displaystyle x>1}}
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    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
    0 references
    Q11306
    test
    Ei ⁡ ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}
    xml-id
    C6.S2.SS1.p3.m2acdec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
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    Cauchy principal value
    test
    ⨍ a b superscript subscript principal-value-integral 𝑎 𝑏 {\displaystyle{\displaystyle\pvint_{\NVar{a}}^{\NVar{b}}}}
    xml-id
    C1.S4.E24.m2aadec
    0 references
     
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