DLMF:2.11.E10 (Q1035)

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DLMF:2.11.E10
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    Statements

    test
    E p ⁡ ( z ) = e - z z ⁢ ∑ s = 0 n - 1 ( - 1 ) s ⁢ ( p ) s z s + ( - 1 ) n ⁢ 2 ⁢ π Γ ⁡ ( p ) ⁢ z p - 1 ⁢ F n + p ⁡ ( z ) , exponential-integral-En 𝑝 𝑧 superscript 𝑒 𝑧 𝑧 superscript subscript 𝑠 0 𝑛 1 superscript 1 𝑠 Pochhammer 𝑝 𝑠 superscript 𝑧 𝑠 superscript 1 𝑛 2 𝜋 Euler-Gamma 𝑝 superscript 𝑧 𝑝 1 terminant-function 𝑛 𝑝 𝑧 {\displaystyle{\displaystyle E_{p}\left(z\right)=\frac{e^{-z}}{z}\sum_{s=0}^{n% -1}(-1)^{s}\frac{{\left(p\right)_{s}}}{z^{s}}+(-1)^{n}\frac{2\pi}{\Gamma\left(% p\right)}z^{p-1}F_{n+p}\left(z\right),}}
    0 references
    DLMF id
    DLMF:2.11.E10
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
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    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
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    generalized exponential integral
    test
    E p ⁡ ( z ) exponential-integral-En 𝑝 𝑧 {\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C8.S19.E1.m2acdec
    0 references
    terminant function
    test
    F p ⁡ ( z ) terminant-function 𝑝 𝑧 {\displaystyle{\displaystyle F_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C2.S11.E11.m2adec
    0 references
     
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