DLMF:6.2.E7 (Q2217)

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DLMF:6.2.E7
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    Statements

    Defining formula
    Ei ⁡ ( ± x ) = - Ein ⁡ ( ∓ x ) + ln ⁡ x + γ . exponential-integral-Ei plus-or-minus 𝑥 complementary-exponential-integral minus-or-plus 𝑥 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\pm x\right)=-\mathrm{Ein}\left(% \mp x\right)+\ln x+\gamma.}}
    0 references
    DLMF id
    DLMF:6.2.E7
    0 references
    Symbols used
    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2aadec
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    complementary exponential integral
    Defining formula
    Ein ⁡ ( z ) complementary-exponential-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ein}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E3.m2abdec
    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.m2abdec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
    Q11307
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C6.S1.XMD1.m1bdec
    0 references
     
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