DLMF:14.24.E4 (Q4957): 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.m2aadec

Revision as of 12:41, 2 January 2020

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DLMF:14.24.E4
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    𝑸 ν , s μ ( z ) = e - s μ π i 𝑸 ν μ ( z ) - π i sin ( s μ π ) sin ( μ π ) Γ ( ν - μ + 1 ) P ν - μ ( z ) , associated-Legendre-black-Q 𝜇 𝜈 𝑠 𝑧 superscript 𝑒 𝑠 𝜇 𝜋 𝑖 associated-Legendre-black-Q 𝜇 𝜈 𝑧 𝜋 𝑖 𝑠 𝜇 𝜋 𝜇 𝜋 Euler-Gamma 𝜈 𝜇 1 Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu,s}\left(z\right)=e^{-s% \mu\pi i}\boldsymbol{Q}^{\mu}_{\nu}\left(z\right)-\frac{\pi i\sin\left(s\mu\pi% \right)}{\sin\left(\mu\pi\right)\Gamma\left(\nu-\mu+1\right)}P^{-\mu}_{\nu}% \left(z\right),}}
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2aadec
    0 references