DLMF:8.20.E2 (Q2715)

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DLMF:8.20.E2
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    Statements

    Defining formula
    E p ⁡ ( z ) ∼ e - z z ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ ( p ) k z k , asymptotic-expansion exponential-integral-En 𝑝 𝑧 superscript 𝑒 𝑧 𝑧 superscript subscript 𝑘 0 superscript 1 𝑘 Pochhammer 𝑝 𝑘 superscript 𝑧 𝑘 {\displaystyle{\displaystyle E_{p}\left(z\right)\sim\frac{e^{-z}}{z}\sum_{k=0}% ^{\infty}(-1)^{k}\frac{{\left(p\right)_{k}}}{z^{k}},}}
    0 references
    DLMF id
    DLMF:8.20.E2
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    constraint
    | ph ⁡ z | ≤ 3 2 ⁢ π - δ phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\frac{3}{2}\pi-\delta}}
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    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
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    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
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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.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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    generalized exponential integral
    Defining formula
    E p ⁡ ( z ) exponential-integral-En 𝑝 𝑧 {\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C8.S19.E1.m2aadec
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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
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    Q11323
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1adec
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    Q11377
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C8.S1.XMD4.m1adec
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    Q11330
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1adec
    0 references
    Q11343
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C8.S1.XMD7.m1dec
    0 references
     
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