DLMF:14.5.E17 (Q4729): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
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.m2addec

Revision as of 01:23, 2 January 2020

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DLMF:14.5.E17
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    Statements

    𝑸 ν ± 1 / 2 ( cosh ξ ) = ( π 2 sinh ξ ) 1 / 2 exp ( - ( ν + 1 2 ) ξ ) Γ ( ν + 3 2 ) . associated-Legendre-black-Q plus-or-minus 1 2 𝜈 𝜉 superscript 𝜋 2 𝜉 1 2 𝜈 1 2 𝜉 Euler-Gamma 𝜈 3 2 {\displaystyle{\displaystyle\boldsymbol{Q}^{\pm 1/2}_{\nu}\left(\cosh\xi\right% )=\left(\frac{\pi}{2\sinh\xi}\right)^{1/2}\frac{\exp\left(-\left(\nu+\frac{1}{% 2}\right)\xi\right)}{\Gamma\left(\nu+\frac{3}{2}\right)}.}}
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    DLMF:14.5.E17
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2addec
    0 references