DLMF:6.2.E5 (Q2215)

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DLMF:6.2.E5
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    Statements

    Defining formula
    Ei ⁡ ( x ) = - ⨍ - x ∞ e - t t ⁢ d t = ⨍ - ∞ x e t t ⁢ d t , exponential-integral-Ei 𝑥 superscript subscript principal-value-integral 𝑥 superscript 𝑒 𝑡 𝑡 𝑡 superscript subscript principal-value-integral 𝑥 superscript 𝑒 𝑡 𝑡 𝑡 {\displaystyle{\displaystyle\mathrm{Ei}\left(x\right)=-\,\pvint_{-x}^{\infty}% \frac{e^{-t}}{t}\mathrm{d}t=\pvint_{-\infty}^{x}\frac{e^{t}}{t}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:6.2.E5
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
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    Q11306
    Defining formula
    Ei ⁡ ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}
    xml-id
    C6.S2.SS1.p3.m2adec
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