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DLMF:6.12.E2 - MaRDI portal

DLMF:6.12.E2 (Q2988)

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DLMF:6.12.E2
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    Statements

    DLMF defining formula
    Ei ⁡ ( x ) ∼ e x x ⁢ ( 1 + 1 ! x + 2 ! x 2 + 3 ! x 3 + ⋯ ) , asymptotic-expansion exponential-integral-Ei 𝑥 superscript 𝑒 𝑥 𝑥 1 1 𝑥 2 superscript 𝑥 2 3 superscript 𝑥 3 ⋯ {\displaystyle{\displaystyle\mathrm{Ei}\left(x\right)\sim\frac{e^{x}}{x}\left(% 1+\frac{1!}{x}+\frac{2!}{x^{2}}+\frac{3!}{x^{3}}+\cdots\right),}}
    0 references
    constraint
    x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}}
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    Symbols used
    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aadec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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    Q11277
    DLMF defining formula
    Ei ⁡ ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}
    xml-id
    C6.S2.SS1.p3.m2adec
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    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
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    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C6.S1.XMD1.m1dec
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    Identifiers

     
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