DLMF:6.15.E2 (Q2307): 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.m2aadec
Property / Symbols used
 
Property / Symbols used: sine integral / rank
 
Normal rank
Property / Symbols used: sine integral / qualifier
 
test:

si ( z ) shifted-sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{si}\left(\NVar{z}\right)}}

\shiftsinint@{\NVar{z}}
Property / Symbols used: sine integral / qualifier
 
xml-id: C6.S2.E10.m2adec
Property / Symbols used
 
Property / Symbols used: Q11308 / rank
 
Normal rank
Property / Symbols used: Q11308 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11308 / qualifier
 
xml-id: C6.S1.XMD3.m1adec

Latest revision as of 01:34, 2 January 2020

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DLMF:6.15.E2
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    Statements

    n = 1 si ( π n ) n = 1 2 π ( ln π - 1 ) , superscript subscript 𝑛 1 shifted-sine-integral 𝜋 𝑛 𝑛 1 2 𝜋 𝜋 1 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}\frac{\mathrm{si}\left(\pi n% \right)}{n}=\tfrac{1}{2}\pi(\ln\pi-1),}}
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
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    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2aadec
    0 references
    si ( z ) shifted-sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{si}\left(\NVar{z}\right)}}
    C6.S2.E10.m2adec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C6.S1.XMD3.m1adec
    0 references