DLMF:31.10.E9 (Q9060): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12495 / rank
 
Normal rank
Property / Symbols used: Q12495 / qualifier
 
Defining formula:

θ 𝜃 {\displaystyle{\displaystyle\theta}}

\theta
Property / Symbols used: Q12495 / qualifier
 
xml-id: C31.S10.XMD6.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12496 / rank
 
Normal rank
Property / Symbols used: Q12496 / qualifier
 
Defining formula:

ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}

\phi
Property / Symbols used: Q12496 / qualifier
 
xml-id: C31.S10.XMD7.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12497 / rank
 
Normal rank
Property / Symbols used: Q12497 / qualifier
 
Defining formula:

σ 𝜎 {\displaystyle{\displaystyle\sigma}}

\sigma
Property / Symbols used: Q12497 / qualifier
 
xml-id: C31.S10.XMD8.m1dec

Latest revision as of 13:36, 2 January 2020

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DLMF:31.10.E9
No description defined

    Statements

    Defining formula
    𝒦 ⁢ ( θ , ϕ ) = P ⁡ { 0 1 ∞ 0 1 2 - δ - σ α cos 2 ⁡ θ 1 - γ 1 2 - ϵ + σ β } ⁢ P ⁡ { 0 1 ∞ 0 0 - 1 2 + δ + σ cos 2 ⁡ ϕ 1 - ϵ 1 - δ - 1 2 + ϵ - σ } , 𝒦 𝜃 italic-ϕ Riemann-P-symbol 0 1 absent 0 1 2 𝛿 𝜎 𝛼 2 𝜃 1 𝛾 1 2 italic-ϵ 𝜎 𝛽 absent Riemann-P-symbol 0 1 absent 0 0 1 2 𝛿 𝜎 2 italic-ϕ 1 italic-ϵ 1 𝛿 1 2 italic-ϵ 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 ⁡ { 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.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
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1ddec
    0 references
    Q12459
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C31.S1.XMD11.m1ddec
    0 references
    Q12460
    Defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C31.S1.XMD12.m1ddec
    0 references
    Q12463
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C31.S1.XMD8.m1bdec
    0 references
    Q12464
    Defining formula
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C31.S1.XMD9.m1bdec
    0 references
    kernel (locally)
    Defining formula
    𝒦 ⁢ ( z , t ) 𝒦 𝑧 𝑡 {\displaystyle{\displaystyle\mathcal{K}(z,t)}}
    xml-id
    C31.S10.XMD4.m1ddec
    0 references
    Q12495
    Defining formula
    θ 𝜃 {\displaystyle{\displaystyle\theta}}
    xml-id
    C31.S10.XMD6.m1bdec
    0 references
    Q12496
    Defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C31.S10.XMD7.m1bdec
    0 references
    Q12497
    Defining formula
    σ 𝜎 {\displaystyle{\displaystyle\sigma}}
    xml-id
    C31.S10.XMD8.m1dec
    0 references
     
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