DLMF:2.5.E15 (Q791): Difference between revisions

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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.m2adec
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
Property / Symbols used
 
Property / Symbols used: Q11000 / rank
 
Normal rank
Property / Symbols used: Q11000 / qualifier
 
test:

a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}

a_{n}
Property / Symbols used: Q11000 / qualifier
 
xml-id: C2.S5.XMD11.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11001 / rank
 
Normal rank
Property / Symbols used: Q11001 / qualifier
 
test:

b n subscript 𝑏 𝑛 {\displaystyle{\displaystyle b_{n}}}

b_{n}
Property / Symbols used: Q11001 / qualifier
 
xml-id: C2.S5.XMD12.m1bdec
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.m1dec
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.m1edec

Latest revision as of 16:03, 1 January 2020

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DLMF:2.5.E15
No description defined

    Statements

    test
    I ⁢ ( x ) = - ∑ s = 0 2 ⁢ n ( a s ⁢ ln ⁡ x + b s ) ⁢ x - s + O ⁡ ( x - 2 ⁢ n - 1 + ϵ ) , 𝐼 𝑥 superscript subscript 𝑠 0 2 𝑛 subscript 𝑎 𝑠 𝑥 subscript 𝑏 𝑠 superscript 𝑥 𝑠 Big-O superscript 𝑥 2 𝑛 1 italic-ϵ {\displaystyle{\displaystyle I(x)=-\sum_{s=0}^{2n}(a_{s}\ln x+b_{s})x^{-s}+O% \left(x^{-2n-1+\epsilon}\right),}}
    0 references
    DLMF id
    DLMF:2.5.E15
    0 references
    constraint
    n = 0 , 1 , 2 , … 𝑛 0 1 2 … {\displaystyle{\displaystyle n=0,1,2,\dots}}
    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
    Q11000
    test
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C2.S5.XMD11.m1cdec
    0 references
    Q11001
    test
    b n subscript 𝑏 𝑛 {\displaystyle{\displaystyle b_{n}}}
    xml-id
    C2.S5.XMD12.m1bdec
    0 references
    Q11002
    test
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C2.S5.XMD13.m1dec
    0 references
    Q10994
    test
    I ⁢ ( x ) 𝐼 𝑥 {\displaystyle{\displaystyle I(x)}}
    xml-id
    C2.S5.XMD5.m1edec
    0 references
     
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