DLMF:6.6.E3 (Q2250)

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DLMF:6.6.E3
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    Statements

    Defining formula
    E 1 ⁡ ( z ) = - ln ⁡ z + e - z ⁢ ∑ n = 0 ∞ z n n ! ⁢ ψ ⁡ ( n + 1 ) , exponential-integral 𝑧 𝑧 superscript 𝑒 𝑧 superscript subscript 𝑛 0 superscript 𝑧 𝑛 𝑛 digamma 𝑛 1 {\displaystyle{\displaystyle E_{1}\left(z\right)=-\ln z+e^{-z}\sum_{n=0}^{% \infty}\frac{z^{n}}{n!}\psi\left(n+1\right),}}
    0 references
    DLMF id
    DLMF:6.6.E3
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    Symbols used
    psi (or digamma) function
    Defining formula
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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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
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
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