DLMF:14.3.E7 (Q4696): Difference between revisions

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Property / constraint
 

μ + ν - 1 , - 2 , - 3 , 𝜇 𝜈 1 2 3 {\displaystyle{\displaystyle\mu+\nu\neq-1,-2,-3,\dots}}

\mu+\nu\neq-1,-2,-3,\dots
Property / constraint: μ + ν - 1 , - 2 , - 3 , 𝜇 𝜈 1 2 3 {\displaystyle{\displaystyle\mu+\nu\neq-1,-2,-3,\dots}} / rank
 
Normal rank

Revision as of 17:51, 30 December 2019

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DLMF:14.3.E7
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    Q ν μ ( x ) = e μ π i π 1 / 2 Γ ( ν + μ + 1 ) ( x 2 - 1 ) μ / 2 2 ν + 1 x ν + μ + 1 𝐅 ( 1 2 ν + 1 2 μ + 1 , 1 2 ν + 1 2 μ + 1 2 ; ν + 3 2 ; 1 x 2 ) , Legendre-Q-second-kind 𝜇 𝜈 𝑥 superscript 𝑒 𝜇 𝜋 𝑖 superscript 𝜋 1 2 Euler-Gamma 𝜈 𝜇 1 superscript superscript 𝑥 2 1 𝜇 2 superscript 2 𝜈 1 superscript 𝑥 𝜈 𝜇 1 scaled-hypergeometric-bold-F 1 2 𝜈 1 2 𝜇 1 1 2 𝜈 1 2 𝜇 1 2 𝜈 3 2 1 superscript 𝑥 2 {\displaystyle{\displaystyle Q^{\mu}_{\nu}\left(x\right)=e^{\mu\pi i}\frac{\pi% ^{1/2}\Gamma\left(\nu+\mu+1\right)\left(x^{2}-1\right)^{\mu/2}}{2^{\nu+1}x^{% \nu+\mu+1}}\mathbf{F}\left(\tfrac{1}{2}\nu+\tfrac{1}{2}\mu+1,\tfrac{1}{2}\nu+% \tfrac{1}{2}\mu+\tfrac{1}{2};\nu+\tfrac{3}{2};\frac{1}{x^{2}}\right),}}
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    DLMF:14.3.E7
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    μ + ν - 1 , - 2 , - 3 , 𝜇 𝜈 1 2 3 {\displaystyle{\displaystyle\mu+\nu\neq-1,-2,-3,\dots}}
    0 references