DLMF:6.12.E1 (Q2289)

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DLMF:6.12.E1
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    Statements

    Defining formula
    E 1 ⁡ ( z ) ∼ e - z z ⁢ ( 1 - 1 ! z + 2 ! z 2 - 3 ! z 3 + ⋯ ) , asymptotic-expansion exponential-integral 𝑧 superscript 𝑒 𝑧 𝑧 1 1 𝑧 2 superscript 𝑧 2 3 superscript 𝑧 3 ⋯ {\displaystyle{\displaystyle E_{1}\left(z\right)\sim\frac{e^{-z}}{z}\left(1-% \frac{1!}{z}+\frac{2!}{z^{2}}-\frac{3!}{z^{3}}+\cdots\right),}}
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    DLMF id
    DLMF:6.12.E1
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    constraint
    | ph ⁡ z | ≤ 3 2 ⁢ π - δ ( < 3 2 ⁢ π ) phase 𝑧 annotated 3 2 𝜋 𝛿 absent 3 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta(<% \tfrac{3}{2}\pi)}}
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    z → ∞ → 𝑧 {\displaystyle{\displaystyle z\to\infty}}
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    | ph ⁡ z | ≤ 3 2 ⁢ π - δ ( < 3 2 ⁢ π ) ph 𝑧 annotated 3 2 𝜋 𝛿 absent 3 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta(<% \tfrac{3}{2}\pi)}}
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    Symbols used
    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.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.m2adec
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