DLMF:6.15.E3 (Q2308): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Euler’s constant / rank
 
Normal rank
Property / Symbols used: Euler’s constant / qualifier
 
test:

γ {\displaystyle{\displaystyle\gamma}}

\EulerConstant
Property / Symbols used: Euler’s constant / qualifier
 
xml-id: C5.S2.E3.m2aadec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: cosine integral / rank
 
Normal rank
Property / Symbols used: cosine integral / qualifier
 
test:

Ci ( z ) cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{z}\right)}}

\cosint@{\NVar{z}}
Property / Symbols used: cosine integral / qualifier
 
xml-id: C6.S2.E11.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.m2abdec
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.m1bdec

Latest revision as of 01:35, 2 January 2020

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DLMF:6.15.E3
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    n = 1 ( - 1 ) n Ci ( 2 π n ) = 1 - ln 2 - 1 2 γ , superscript subscript 𝑛 1 superscript 1 𝑛 cosine-integral 2 𝜋 𝑛 1 2 1 2 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}(-1)^{n}\mathrm{Ci}\left(2\pi n% \right)=1-\ln 2-\tfrac{1}{2}\gamma,}}
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    γ {\displaystyle{\displaystyle\gamma}}
    C5.S2.E3.m2aadec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2abdec
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    Ci ( z ) cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{z}\right)}}
    C6.S2.E11.m2aadec
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    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2abdec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C6.S1.XMD3.m1bdec
    0 references