DLMF:14.9.E9 (Q4800): Difference between revisions

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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.m2aedec

Revision as of 01:37, 2 January 2020

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DLMF:14.9.E9
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    2 Γ ( ν + μ + 1 ) Γ ( μ - ν ) 𝖰 ν μ ( x ) = - cos ( ν π ) 𝖯 ν - μ ( x ) + cos ( μ π ) 𝖯 ν - μ ( - x ) , 2 Euler-Gamma 𝜈 𝜇 1 Euler-Gamma 𝜇 𝜈 Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 𝜈 𝜋 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 𝜇 𝜋 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\frac{2}{\Gamma\left(\nu+\mu+1\right)\Gamma\left(% \mu-\nu\right)}\mathsf{Q}^{\mu}_{\nu}\left(x\right)=-\cos\left(\nu\pi\right)% \mathsf{P}^{-\mu}_{\nu}\left(x\right)+\cos\left(\mu\pi\right)\mathsf{P}^{-\mu}% _{\nu}\left(-x\right),}}
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    DLMF:14.9.E9
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2aedec
    0 references