DLMF:6.2.E10 (Q2220): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aedec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

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

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: sine integral / rank
 
Normal rank
Property / Symbols used: sine integral / qualifier
 
Defining formula:

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

\sinint@{\NVar{z}}
Property / Symbols used: sine integral / qualifier
 
xml-id: C6.S2.E9.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11305 / rank
 
Normal rank
Property / Symbols used: Q11305 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11305 / qualifier
 
xml-id: C6.S1.XMD2.m1edec

Latest revision as of 01:20, 2 January 2020

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English
DLMF:6.2.E10
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    Statements

    si ( z ) = - z sin t t d t = Si ( z ) - 1 2 π . shifted-sine-integral 𝑧 superscript subscript 𝑧 𝑡 𝑡 𝑡 sine-integral 𝑧 1 2 𝜋 {\displaystyle{\displaystyle\mathrm{si}\left(z\right)=-\int_{z}^{\infty}\frac{% \sin t}{t}\mathrm{d}t=\mathrm{Si}\left(z\right)-\tfrac{1}{2}\pi.}}
    0 references
    DLMF:6.2.E10
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1agdec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aedec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2aadec
    0 references
    Si ( z ) sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{z}\right)}}
    C6.S2.E9.m2aadec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C6.S1.XMD2.m1edec
    0 references