DLMF:31.10.E22 (Q9077): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Riemann’s $$P$$ -symbol for solutions of the generalized hypergeometric differential equation / rank
 
Normal rank
Property / Symbols used: Riemann’s $$P$$ -symbol for solutions of the generalized hypergeometric differential equation / qualifier
 
Defining formula:

P { α β γ a 1 b 1 c 1 z a 2 b 2 c 2 } Riemann-P-symbol 𝛼 𝛽 𝛾 absent subscript 𝑎 1 subscript 𝑏 1 subscript 𝑐 1 𝑧 subscript 𝑎 2 subscript 𝑏 2 subscript 𝑐 2 absent {\displaystyle{\displaystyle P\NVar{\begin{Bmatrix}\alpha&\beta&\gamma&\\ a_{1}&b_{1}&c_{1}&z\\ a_{2}&b_{2}&c_{2}&\end{Bmatrix}}}}

\RiemannsymP@{\NVar{\begin{Bmatrix}\alpha&\beta&\gamma&\\ a_{1}&b_{1}&c_{1}&z\\ a_{2}&b_{2}&c_{2}&\end{Bmatrix}}}
Property / Symbols used: Riemann’s $$P$$ -symbol for solutions of the generalized hypergeometric differential equation / qualifier
 
xml-id: C15.S11.E3.m2abdec

Revision as of 13:39, 2 January 2020

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DLMF:31.10.E22
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    𝒦 ( r , θ , ϕ ) = r m sin 2 p θ P { 0 1 0 0 a cos 2 θ 1 2 ( 3 - γ ) c b } P { 0 1 0 0 a cos 2 ϕ 1 - ϵ 1 - δ b } , 𝒦 𝑟 𝜃 italic-ϕ superscript 𝑟 𝑚 2 𝑝 𝜃 Riemann-P-symbol 0 1 absent 0 0 𝑎 2 𝜃 1 2 3 𝛾 𝑐 𝑏 absent Riemann-P-symbol 0 1 absent 0 0 superscript 𝑎 2 italic-ϕ 1 italic-ϵ 1 𝛿 superscript 𝑏 absent {\displaystyle{\displaystyle\mathcal{K}(r,\theta,\phi)=r^{m}{\sin^{2p}}\theta P% \begin{Bmatrix}0&1&\infty&\\ 0&0&a&{\cos^{2}}\theta\\ \tfrac{1}{2}(3-\gamma)&c&b&\end{Bmatrix}\*P\begin{Bmatrix}0&1&\infty&\\ 0&0&a^{\prime}&{\cos^{2}}\phi\\ 1-\epsilon&1-\delta&b^{\prime}&\end{Bmatrix},}}
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    DLMF:31.10.E22
    0 references
    P { α β γ a 1 b 1 c 1 z a 2 b 2 c 2 } Riemann-P-symbol 𝛼 𝛽 𝛾 absent subscript 𝑎 1 subscript 𝑏 1 subscript 𝑐 1 𝑧 subscript 𝑎 2 subscript 𝑏 2 subscript 𝑐 2 absent {\displaystyle{\displaystyle P\NVar{\begin{Bmatrix}\alpha&\beta&\gamma&\\ a_{1}&b_{1}&c_{1}&z\\ a_{2}&b_{2}&c_{2}&\end{Bmatrix}}}}
    C15.S11.E3.m2abdec
    0 references