DLMF:14.2.E11 (Q4689): 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.m2aedec

Revision as of 01:12, 2 January 2020

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DLMF:14.2.E11
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    P ν + 1 μ ( x ) Q ν μ ( x ) - P ν μ ( x ) Q ν + 1 μ ( x ) = e μ π i Γ ( ν + μ + 1 ) Γ ( ν - μ + 2 ) . Legendre-P-first-kind 𝜇 𝜈 1 𝑥 Legendre-Q-second-kind 𝜇 𝜈 𝑥 Legendre-P-first-kind 𝜇 𝜈 𝑥 Legendre-Q-second-kind 𝜇 𝜈 1 𝑥 superscript 𝑒 𝜇 𝜋 𝑖 Euler-Gamma 𝜈 𝜇 1 Euler-Gamma 𝜈 𝜇 2 {\displaystyle{\displaystyle P^{\mu}_{\nu+1}\left(x\right)Q^{\mu}_{\nu}\left(x% \right)-P^{\mu}_{\nu}\left(x\right)Q^{\mu}_{\nu+1}\left(x\right)=e^{\mu\pi i}% \frac{\Gamma\left(\nu+\mu+1\right)}{\Gamma\left(\nu-\mu+2\right)}.}}
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    DLMF:14.2.E11
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2aedec
    0 references