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DLMF:6.2.E5 - MaRDI portal

DLMF:6.2.E5 (Q2913)

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DLMF:6.2.E5
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    Statements

    DLMF 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
    Symbols used
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    Q11277
    DLMF defining formula
    Ei ⁡ ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}
    xml-id
    C6.S2.SS1.p3.m2adec
    0 references
    Cauchy principal value
    DLMF defining formula
    ⨍ a b superscript subscript principal-value-integral 𝑎 𝑏 {\displaystyle{\displaystyle\pvint_{\NVar{a}}^{\NVar{b}}}}
    xml-id
    C1.S4.E24.m2adec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C6.S1.XMD1.m1dec
    0 references
     
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