DLMF:4.10.E7 (Q1622): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: logarithmic integral / rank
 
Normal rank
Property / Symbols used: logarithmic integral / qualifier
 
test:

li ( x ) logarithmic-integral 𝑥 {\displaystyle{\displaystyle\mathrm{li}\left(\NVar{x}\right)}}

\logint@{\NVar{x}}
Property / Symbols used: logarithmic integral / qualifier
 
xml-id: C6.S2.E8.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.m2afdec
Property / Symbols used
 
Property / Symbols used: Cauchy principal value / rank
 
Normal rank
Property / Symbols used: Cauchy principal value / qualifier
 
test:

a b superscript subscript principal-value-integral 𝑎 𝑏 {\displaystyle{\displaystyle\pvint_{\NVar{a}}^{\NVar{b}}}}

\pvint_{\NVar{a}}^{\NVar{b}}
Property / Symbols used: Cauchy principal value / qualifier
 
xml-id: C1.S4.E24.m2adec
Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1dec

Latest revision as of 17:14, 1 January 2020

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DLMF:4.10.E7
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    Statements

    0 x d t ln t = li ( x ) , superscript subscript principal-value-integral 0 𝑥 𝑡 𝑡 logarithmic-integral 𝑥 {\displaystyle{\displaystyle\pvint_{0}^{x}\frac{\mathrm{d}t}{\ln t}=\mathrm{li% }\left(x\right),}}
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    x > 1 𝑥 1 {\displaystyle{\displaystyle x>1}}
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1afdec
    0 references
    li ( x ) logarithmic-integral 𝑥 {\displaystyle{\displaystyle\mathrm{li}\left(\NVar{x}\right)}}
    C6.S2.E8.m2adec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2afdec
    0 references
    a b superscript subscript principal-value-integral 𝑎 𝑏 {\displaystyle{\displaystyle\pvint_{\NVar{a}}^{\NVar{b}}}}
    C1.S4.E24.m2adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C4.S1.XMD6.m1dec
    0 references