DLMF:14.5.E3 (Q4715): Difference between revisions

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ν + μ - 1 , - 3 , - 5 , 𝜈 𝜇 1 3 5 {\displaystyle{\displaystyle\nu+\mu\neq-1,-3,-5,\dots}}

\nu+\mu\neq-1,-3,-5,\dots
Property / constraint: ν + μ - 1 , - 3 , - 5 , 𝜈 𝜇 1 3 5 {\displaystyle{\displaystyle\nu+\mu\neq-1,-3,-5,\dots}} / rank
 
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Revision as of 17:51, 30 December 2019

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DLMF:14.5.E3
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    𝖰 ν μ ( 0 ) = - 2 μ - 1 π 1 / 2 sin ( 1 2 ( ν + μ ) π ) Γ ( 1 2 ν + 1 2 μ + 1 2 ) Γ ( 1 2 ν - 1 2 μ + 1 ) , Ferrers-Legendre-Q-first-kind 𝜇 𝜈 0 superscript 2 𝜇 1 superscript 𝜋 1 2 1 2 𝜈 𝜇 𝜋 Euler-Gamma 1 2 𝜈 1 2 𝜇 1 2 Euler-Gamma 1 2 𝜈 1 2 𝜇 1 {\displaystyle{\displaystyle\mathsf{Q}^{\mu}_{\nu}\left(0\right)=-\frac{2^{\mu% -1}\pi^{1/2}\sin\left(\frac{1}{2}(\nu+\mu)\pi\right)\Gamma\left(\frac{1}{2}\nu% +\frac{1}{2}\mu+\frac{1}{2}\right)}{\Gamma\left(\frac{1}{2}\nu-\frac{1}{2}\mu+% 1\right)},}}
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    DLMF:14.5.E3
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    ν + μ - 1 , - 3 , - 5 , 𝜈 𝜇 1 3 5 {\displaystyle{\displaystyle\nu+\mu\neq-1,-3,-5,\dots}}
    0 references