DLMF:31.10.E22 (Q9077)

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DLMF:31.10.E22
No description defined

    Statements

    Defining formula
    𝒦 ⁒ ( r , ΞΈ , Ο• ) = r m ⁒ sin 2 ⁒ p ⁑ ΞΈ ⁒ P ⁑ { 0 1 ∞ 0 0 a cos 2 ⁑ ΞΈ 1 2 ⁒ ( 3 - Ξ³ ) c b } ⁒ P ⁑ { 0 1 ∞ 0 0 a β€² cos 2 ⁑ Ο• 1 - Ο΅ 1 - Ξ΄ b β€² } , 𝒦 π‘Ÿ πœƒ italic-Ο• superscript π‘Ÿ π‘š 2 𝑝 πœƒ Riemann-P-symbol 0 1 absent 0 0 π‘Ž 2 πœƒ 1 2 3 𝛾 𝑐 𝑏 absent Riemann-P-symbol 0 1 absent 0 0 superscript π‘Ž β€² 2 italic-Ο• 1 italic-Ο΅ 1 𝛿 superscript 𝑏 β€² 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},}}
    0 references
    DLMF id
    DLMF:31.10.E22
    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.m2abdec
    0 references
    cosine function
    Defining formula
    cos ⁑ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2acdec
    0 references
    sine function
    Defining formula
    sin ⁑ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2addec
    0 references
    Q12458
    Defining formula
    Ξ³ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1kdec
    0 references
    Q12459
    Defining formula
    Ξ΄ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C31.S1.XMD11.m1kdec
    0 references
    Q12460
    Defining formula
    Ο΅ italic-Ο΅ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C31.S1.XMD12.m1kdec
    0 references
    Q12483
    Defining formula
    m π‘š {\displaystyle{\displaystyle m}}
    xml-id
    C31.S1.XMD4.m1dec
    0 references
    Q12461
    Defining formula
    a π‘Ž {\displaystyle{\displaystyle a}}
    xml-id
    C31.S1.XMD6.m1hdec
    0 references
    kernel (locally)
    Defining formula
    𝒦 ⁒ ( z ; s , t ) 𝒦 𝑧 𝑠 𝑑 {\displaystyle{\displaystyle\mathcal{K}(z;s,t)}}
    xml-id
    C31.S10.XMD13.m1gdec
    0 references
    Q12503
    Defining formula
    r π‘Ÿ {\displaystyle{\displaystyle r}}
    xml-id
    C31.S10.XMD18.m1bdec
    0 references
    Q12504
    Defining formula
    ΞΈ πœƒ {\displaystyle{\displaystyle\theta}}
    xml-id
    C31.S10.XMD19.m1bdec
    0 references
    Q12505
    Defining formula
    Ο• italic-Ο• {\displaystyle{\displaystyle\phi}}
    xml-id
    C31.S10.XMD20.m1bdec
    0 references
    Q12506
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C31.S10.XMD21.m1dec
    0 references
    Q12507
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C31.S10.XMD22.m1dec
    0 references
     
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