DLMF:6.14.E5 (Q2303): Difference between revisions

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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.m2adec
Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
test:

cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2adec
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: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1addec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3addec
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.m2aadec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
test:

sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2adec

Latest revision as of 01:34, 2 January 2020

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DLMF:6.14.E5
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    Statements

    0 cos t Ci ( t ) d t = 0 sin t si ( t ) d t = - 1 4 π , superscript subscript 0 𝑡 cosine-integral 𝑡 𝑡 superscript subscript 0 𝑡 shifted-sine-integral 𝑡 𝑡 1 4 𝜋 {\displaystyle{\displaystyle\int_{0}^{\infty}\cos t\mathrm{Ci}\left(t\right)% \mathrm{d}t=\int_{0}^{\infty}\sin t\mathrm{si}\left(t\right)\mathrm{d}t=-% \tfrac{1}{4}\pi,}}
    0 references
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2adec
    0 references
    Ci ( z ) cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{z}\right)}}
    C6.S2.E11.m2aadec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1addec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3addec
    0 references
    si ( z ) shifted-sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{si}\left(\NVar{z}\right)}}
    C6.S2.E10.m2aadec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2adec
    0 references