DLMF:6.2.E6 (Q2216)

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DLMF:6.2.E6
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    Statements

    Defining formula
    Ei ⁡ ( - x ) = - ∫ x ∞ e - t t ⁢ d t = - E 1 ⁡ ( x ) , exponential-integral-Ei 𝑥 superscript subscript 𝑥 superscript 𝑒 𝑡 𝑡 𝑡 exponential-integral 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(-x\right)=-\int_{x}^{\infty}\frac% {e^{-t}}{t}\mathrm{d}t=-E_{1}\left(x\right),}}
    0 references
    DLMF id
    DLMF:6.2.E6
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
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    exponential integral
    Defining formula
    E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E1.m2acdec
    0 references
    Q11306
    Defining formula
    Ei ⁡ ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}
    xml-id
    C6.S2.SS1.p3.m2aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    Q11307
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C6.S1.XMD1.m1adec
    0 references
     
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