DLMF:14.9.E12 (Q4804): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

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.m2afdec

Revision as of 00:37, 2 January 2020

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DLMF:14.9.E12
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    cos ( ν π ) P ν - μ ( x ) = - 𝑸 ν μ ( x ) Γ ( μ - ν ) + 𝑸 - ν - 1 μ ( x ) Γ ( ν + μ + 1 ) . 𝜈 𝜋 Legendre-P-first-kind 𝜇 𝜈 𝑥 associated-Legendre-black-Q 𝜇 𝜈 𝑥 Euler-Gamma 𝜇 𝜈 associated-Legendre-black-Q 𝜇 𝜈 1 𝑥 Euler-Gamma 𝜈 𝜇 1 {\displaystyle{\displaystyle\cos\left(\nu\pi\right)P^{-\mu}_{\nu}\left(x\right% )=-\frac{\boldsymbol{Q}^{\mu}_{\nu}\left(x\right)}{\Gamma\left(\mu-\nu\right)}% +\frac{\boldsymbol{Q}^{\mu}_{-\nu-1}\left(x\right)}{\Gamma\left(\nu+\mu+1% \right)}.}}
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2afdec
    0 references