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

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Property / Symbols used
 
Property / Symbols used: Q12507 / rank
 
Normal rank
Property / Symbols used: Q12507 / qualifier
 
Defining formula:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q12507 / qualifier
 
xml-id: C31.S10.XMD22.m1dec

Latest revision as of 13:39, 2 January 2020

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DLMF:31.10.E22
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    Statements

    Defining formula
    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},}}
    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 ⁡ { 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}}}}
    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
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1kdec
    0 references
    Q12459
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C31.S1.XMD11.m1kdec
    0 references
    Q12460
    Defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C31.S1.XMD12.m1kdec
    0 references
    Q12483
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C31.S1.XMD4.m1dec
    0 references
    Q12461
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C31.S1.XMD6.m1hdec
    0 references
    kernel (locally)
    Defining formula
    𝒦 ⁢ ( z ; s , t ) 𝒦 𝑧 𝑠 𝑡 {\displaystyle{\displaystyle\mathcal{K}(z;s,t)}}
    xml-id
    C31.S10.XMD13.m1gdec
    0 references
    Q12503
    Defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C31.S10.XMD18.m1bdec
    0 references
    Q12504
    Defining formula
    θ 𝜃 {\displaystyle{\displaystyle\theta}}
    xml-id
    C31.S10.XMD19.m1bdec
    0 references
    Q12505
    Defining formula
    ϕ italic-ϕ {\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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