DLMF:31.10.E9 (Q9060)

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DLMF:31.10.E9
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    Statements

    Defining formula
    𝒦 ⁒ ( ΞΈ , Ο• ) = P ⁑ { 0 1 ∞ 0 1 2 - Ξ΄ - Οƒ Ξ± cos 2 ⁑ ΞΈ 1 - Ξ³ 1 2 - Ο΅ + Οƒ Ξ² } ⁒ P ⁑ { 0 1 ∞ 0 0 - 1 2 + Ξ΄ + Οƒ cos 2 ⁑ Ο• 1 - Ο΅ 1 - Ξ΄ - 1 2 + Ο΅ - Οƒ } , 𝒦 πœƒ italic-Ο• Riemann-P-symbol 0 1 absent 0 1 2 𝛿 𝜎 𝛼 2 πœƒ 1 𝛾 1 2 italic-Ο΅ 𝜎 𝛽 absent Riemann-P-symbol 0 1 absent 0 0 1 2 𝛿 𝜎 2 italic-Ο• 1 italic-Ο΅ 1 𝛿 1 2 italic-Ο΅ 𝜎 absent {\displaystyle{\displaystyle\mathcal{K}(\theta,\phi)=P\begin{Bmatrix}0&1&% \infty&\\ 0&\frac{1}{2}-\delta-\sigma&\alpha&{\cos^{2}}\theta\\ 1-\gamma&\frac{1}{2}-\epsilon+\sigma&\beta&\end{Bmatrix}\*P\begin{Bmatrix}0&1&% \infty&\\ 0&0&-\frac{1}{2}+\delta+\sigma&{\cos^{2}}\phi\\ 1-\epsilon&1-\delta&-\frac{1}{2}+\epsilon-\sigma&\end{Bmatrix},}}
    0 references
    DLMF id
    DLMF:31.10.E9
    0 references
    Symbols used
    Riemann’s $$P$$ -symbol for solutions of the generalized hypergeometric differential equation
    Defining formula
    P ⁑ { Ξ± Ξ² Ξ³ a 1 b 1 c 1 z a 2 b 2 c 2 } Riemann-P-symbol 𝛼 𝛽 𝛾 absent subscript π‘Ž 1 subscript 𝑏 1 subscript 𝑐 1 𝑧 subscript π‘Ž 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}}}}
    xml-id
    C15.S11.E3.m2adec
    0 references
    cosine function
    Defining formula
    cos ⁑ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    Q12458
    Defining formula
    Ξ³ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1ddec
    0 references
    Q12459
    Defining formula
    Ξ΄ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C31.S1.XMD11.m1ddec
    0 references
    Q12460
    Defining formula
    Ο΅ italic-Ο΅ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C31.S1.XMD12.m1ddec
    0 references
    Q12463
    Defining formula
    Ξ± 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C31.S1.XMD8.m1bdec
    0 references
     
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