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

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Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
Defining formula:

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2aadec

Revision as of 13:36, 2 January 2020

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DLMF:31.10.E9
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    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
     
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