DLMF:2.7.E32 (Q926): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2abdec

Latest revision as of 16:24, 1 January 2020

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DLMF:2.7.E32
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    Statements

    test
    f 1 / 2 = x 1 / 2 + 1 2 ⁢ x - 1 / 2 ⁢ ln ⁡ x + O ⁡ ( x - 3 / 2 ⁢ ( ln ⁡ x ) 2 ) , superscript 𝑓 1 2 superscript 𝑥 1 2 1 2 superscript 𝑥 1 2 𝑥 Big-O superscript 𝑥 3 2 superscript 𝑥 2 {\displaystyle{\displaystyle f^{1/2}=x^{1/2}+\tfrac{1}{2}x^{-1/2}\ln x+O\left(% x^{-3/2}(\ln x)^{2}\right),}}
    0 references
    DLMF id
    DLMF:2.7.E32
    0 references
    Symbols used
    order not exceeding
    test
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
    0 references
     
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