DLMF:2.5.E16 (Q792): Difference between revisions

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imported>Admin
 
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Property / Symbols used
 
Property / Symbols used: order not exceeding / rank
 
Normal rank
Property / Symbols used: order not exceeding / qualifier
 
test:

O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

\bigO@{\NVar{x}}
Property / Symbols used: order not exceeding / qualifier
 
xml-id: C2.S1.E3.m2aadec
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.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11002 / rank
 
Normal rank
Property / Symbols used: Q11002 / qualifier
 
test:

ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}

\epsilon
Property / Symbols used: Q11002 / qualifier
 
xml-id: C2.S5.XMD13.m1adec
Property / Symbols used
 
Property / Symbols used: Q10993 / rank
 
Normal rank
Property / Symbols used: Q10993 / qualifier
 
test:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q10993 / qualifier
 
xml-id: C2.S5.XMD4.m1cdec
Property / Symbols used
 
Property / Symbols used: Q10994 / rank
 
Normal rank
Property / Symbols used: Q10994 / qualifier
 
test:

I ⁢ ( x ) 𝐼 𝑥 {\displaystyle{\displaystyle I(x)}}

I(x)
Property / Symbols used: Q10994 / qualifier
 
xml-id: C2.S5.XMD5.m1fdec
Property / Symbols used
 
Property / Symbols used: Q10996 / rank
 
Normal rank
Property / Symbols used: Q10996 / qualifier
 
test:

d 𝑑 {\displaystyle{\displaystyle d}}

d
Property / Symbols used: Q10996 / qualifier
 
xml-id: C2.S5.XMD7.m1bdec

Latest revision as of 16:04, 1 January 2020

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English
DLMF:2.5.E16
No description defined

    Statements

    test
    I ⁢ ( x ) = ∑ s = 0 n - 1 ( c s ⁢ ln ⁡ x + d s ) ⁢ x - 2 ⁢ s - 1 + O ⁡ ( x - 2 ⁢ n - 1 + ϵ ) , 𝐼 𝑥 superscript subscript 𝑠 0 𝑛 1 subscript 𝑐 𝑠 𝑥 subscript 𝑑 𝑠 superscript 𝑥 2 𝑠 1 Big-O superscript 𝑥 2 𝑛 1 italic-ϵ {\displaystyle{\displaystyle I(x)=\sum_{s=0}^{n-1}(c_{s}\ln x+d_{s})x^{-2s-1}+% O\left(x^{-2n-1+\epsilon}\right),}}
    0 references
    DLMF id
    DLMF:2.5.E16
    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.m2aadec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
    0 references
    Q11002
    test
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C2.S5.XMD13.m1adec
    0 references
    Q10993
    test
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C2.S5.XMD4.m1cdec
    0 references
    Q10994
    test
    I ⁢ ( x ) 𝐼 𝑥 {\displaystyle{\displaystyle I(x)}}
    xml-id
    C2.S5.XMD5.m1fdec
    0 references
    Q10996
    test
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C2.S5.XMD7.m1bdec
    0 references
     
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