DLMF:6.2.E2 (Q2212)

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DLMF:6.2.E2
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    Statements

    Defining formula
    E 1 ⁡ ( z ) = e - z ⁢ ∫ 0 ∞ e - t t + z ⁢ d t , exponential-integral 𝑧 superscript 𝑒 𝑧 superscript subscript 0 superscript 𝑒 𝑡 𝑡 𝑧 𝑡 {\displaystyle{\displaystyle E_{1}\left(z\right)=e^{-z}\int_{0}^{\infty}\frac{% e^{-t}}{t+z}\mathrm{d}t,}}
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    DLMF id
    DLMF:6.2.E2
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    constraint
    | ph ⁡ z | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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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.m2aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    Q11305
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1adec
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