DLMF:6.4.E3 (Q2236)

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DLMF:6.4.E3
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    Statements

    Defining formula
    E 1 ⁡ ( z ⁢ e ± π ⁢ i ) = Ein ⁡ ( - z ) - ln ⁡ z - γ ∓ π ⁢ i , exponential-integral 𝑧 superscript 𝑒 plus-or-minus 𝜋 𝑖 minus-or-plus complementary-exponential-integral 𝑧 𝑧 𝜋 𝑖 {\displaystyle{\displaystyle E_{1}\left(ze^{\pm\pi i}\right)=\mathrm{Ein}\left% (-z\right)-\ln z-\gamma\mp\pi i,}}
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    DLMF id
    DLMF:6.4.E3
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    constraint
    | ph ⁡ z | ≤ π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi}}
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    Symbols used
    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2aadec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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