DLMF:35.7.E2 (Q9813): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: Jacobi function of matrix argument / rank
 
Normal rank

Revision as of 16:29, 30 December 2019

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DLMF:35.7.E2
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    Defining formula
    P ν ( γ , δ ) ⁡ ( 𝐓 ) = Γ m ⁡ ( γ + ν + 1 2 ⁢ ( m + 1 ) ) Γ m ⁡ ( γ + 1 2 ⁢ ( m + 1 ) ) ⁢ F 1 2 ⁡ ( - ν , γ + δ + ν + 1 2 ⁢ ( m + 1 ) γ + 1 2 ⁢ ( m + 1 ) ; 𝐓 ) , Jacobi-function-of-matrix-P 𝛾 𝛿 𝜈 𝐓 multivariate-Euler-Gamma 𝑚 𝛾 𝜈 1 2 𝑚 1 multivariate-Euler-Gamma 𝑚 𝛾 1 2 𝑚 1 Gauss-hypergeometric-of-matrix-pFq 2 1 𝜈 𝛾 𝛿 𝜈 1 2 𝑚 1 𝛾 1 2 𝑚 1 𝐓 {\displaystyle{\displaystyle P^{(\gamma,\delta)}_{\nu}\left(\mathbf{T}\right)=% \frac{\Gamma_{m}\left(\gamma+\nu+\frac{1}{2}(m+1)\right)}{\Gamma_{m}\left(% \gamma+\frac{1}{2}(m+1)\right)}\*{{}_{2}F_{1}}\left({-\nu,\gamma+\delta+\nu+% \frac{1}{2}(m+1)\atop\gamma+\frac{1}{2}(m+1)};\mathbf{T}\right),}}
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    DLMF id
    DLMF:35.7.E2
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