DLMF:8.21.E12 (Q2734): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
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
 
Defining formula:

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.m2aedec
Property / Symbols used
 
Property / Symbols used: generalized sine integral / rank
 
Normal rank
Property / Symbols used: generalized sine integral / qualifier
 
Defining formula:

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

\gensinint@{\NVar{a}}{\NVar{z}}
Property / Symbols used: generalized sine integral / qualifier
 
xml-id: C8.S21.E2.m3addec
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.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1idec

Latest revision as of 14:17, 2 January 2020

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DLMF:8.21.E12
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    Statements

    Si ( a , ) = Γ ( a ) sin ( 1 2 π a ) , generalized-sine-integral-Si 𝑎 Euler-Gamma 𝑎 1 2 𝜋 𝑎 {\displaystyle{\displaystyle\mathrm{Si}\left(a,\infty\right)=\Gamma\left(a% \right)\sin\left(\tfrac{1}{2}\pi a\right),}}
    0 references
    DLMF:8.21.E12
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    a - 1 , - 3 , - 5 , 𝑎 1 3 5 {\displaystyle{\displaystyle a\neq-1,-3,-5,\dots}}
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2acdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aedec
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    Si ( a , z ) generalized-sine-integral-Si 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{a},\NVar{z}\right)}}
    C8.S21.E2.m3addec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2acdec
    0 references
    a 𝑎 {\displaystyle{\displaystyle a}}
    C8.S1.XMD3.m1idec
    0 references