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

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Property / constraint
 

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
 
Normal rank

Revision as of 16:51, 30 December 2019

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DLMF:14.5.E3
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    Statements

    test
    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)},}}
    0 references
    DLMF id
    DLMF:14.5.E3
    0 references
    constraint
    ν + μ ≠ - 1 , - 3 , - 5 , … 𝜈 𝜇 1 3 5 … {\displaystyle{\displaystyle\nu+\mu\neq-1,-3,-5,\dots}}
    0 references
     
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