DLMF:5.5.E3 (Q2061): 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: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.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
 
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.m2adec
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.m2adec
Property / Symbols used
 
Property / Symbols used: Q11273 / rank
 
Normal rank
Property / Symbols used: Q11273 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11273 / qualifier
 
xml-id: C5.S1.XMD7.m1bdec

Latest revision as of 19:31, 1 January 2020

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DLMF:5.5.E3
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    Statements

    Γ ( z ) Γ ( 1 - z ) = π / sin ( π z ) , Euler-Gamma 𝑧 Euler-Gamma 1 𝑧 𝜋 𝜋 𝑧 {\displaystyle{\displaystyle\Gamma\left(z\right)\Gamma\left(1-z\right)=\pi/% \sin\left(\pi z\right),}}
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    DLMF:5.5.E3
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    z 0 , ± 1 , 𝑧 0 plus-or-minus 1 {\displaystyle{\displaystyle z\neq 0,\pm 1,\dots}}
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2aadec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
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    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2adec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C5.S1.XMD7.m1bdec
    0 references