DLMF:18.19.E3 (Q5833): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1cdec

Latest revision as of 01:29, 2 January 2020

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DLMF:18.19.E3
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    Statements

    w ( x ) = w ( x ; a , b , a ¯ , b ¯ ) = | Γ ( a + i x ) Γ ( b + i x ) | 2 , 𝑤 𝑥 𝑤 𝑥 𝑎 𝑏 𝑎 𝑏 superscript Euler-Gamma 𝑎 imaginary-unit 𝑥 Euler-Gamma 𝑏 imaginary-unit 𝑥 2 {\displaystyle{\displaystyle w(x)=w(x;a,b,\overline{a},\overline{b})=|\Gamma% \left(a+\mathrm{i}x\right)\Gamma\left(b+\mathrm{i}x\right)|^{2},}}
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    DLMF:18.19.E3
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2aadec
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    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    C1.S9.E11.m2abdec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aadec
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    w ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}
    C18.S1.XMD10.m1adec
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    x 𝑥 {\displaystyle{\displaystyle x}}
    C18.S2.XMD3.m1cdec
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