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DLMF:4.4.E13 - MaRDI portal

DLMF:4.4.E13 (Q1590)

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DLMF:4.4.E13
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    Statements

    DLMF defining formula
    lim x → ∞ ⁡ x - a ⁢ ln ⁡ x = 0 , subscript → 𝑥 superscript 𝑥 𝑎 𝑥 0 {\displaystyle{\displaystyle\lim_{x\to\infty}x^{-a}\ln x=0,}}
    0 references
    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
    0 references
    Symbols used
    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
    0 references
    real part
    DLMF defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
    real or complex constant
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C4.S1.XMD4.m1dec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1dec
    0 references

    Identifiers

     
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