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DLMF:8.20.E6 - MaRDI portal

DLMF:8.20.E6 (Q3419)

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DLMF:8.20.E6
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    Statements

    DLMF defining formula
    E p ⁡ ( λ ⁢ p ) ∼ e - λ ⁢ p ( λ + 1 ) ⁢ p ⁢ ∑ k = 0 ∞ A k ⁢ ( λ ) ( λ + 1 ) 2 ⁢ k ⁢ 1 p k , asymptotic-expansion exponential-integral-En 𝑝 𝜆 𝑝 superscript 𝑒 𝜆 𝑝 𝜆 1 𝑝 superscript subscript 𝑘 0 subscript 𝐴 𝑘 𝜆 superscript 𝜆 1 2 𝑘 1 superscript 𝑝 𝑘 {\displaystyle{\displaystyle E_{p}\left(\lambda p\right)\sim\frac{e^{-\lambda p% }}{(\lambda+1)p}\sum_{k=0}^{\infty}\frac{A_{k}(\lambda)}{(\lambda+1)^{2k}}% \frac{1}{p^{k}},}}
    0 references
    Symbols used
    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11abdec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
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    generalized exponential integral
    DLMF defining formula
    E p ⁡ ( z ) exponential-integral-En 𝑝 𝑧 {\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C8.S19.E1.m2acdec
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    parameter
    DLMF defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C8.S1.XMD4.m1cdec
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    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1ddec
    0 references
    A k ( λ )
    DLMF defining formula
    A k ⁢ ( λ ) subscript 𝐴 𝑘 𝜆 {\displaystyle{\displaystyle A_{k}(\lambda)}}
    xml-id
    C8.S20.XMD1.m1bdec
    0 references

    Identifiers

     
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