DLMF:18.26.E3 (Q5933): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11785 / rank
 
Normal rank
Property / Symbols used: Q11785 / qualifier
 
Defining formula:

R n ⁡ ( x ; α , β , γ , ) Racah-polynomial-R 𝑛 𝑥 𝛼 𝛽 𝛾 {\displaystyle{\displaystyle R_{\NVar{n}}\left(\NVar{x};\NVar{\alpha},\NVar{% \beta},\NVar{\gamma},\right)\)\@add@PDF@RDFa@triples\end{document}}}

\RacahpolyR{\NVar{n}}@{\NVar{x}}{\NVar{\alpha}}{\NVar{\beta}}{\NVar{\gamma}}{% \NVar{\delta}}
Property / Symbols used: Q11785 / qualifier
 
xml-id: C18.S25.T1.t1.r4.m2adec
Property / Symbols used
 
Property / Symbols used: Q11743 / rank
 
Normal rank
Property / Symbols used: Q11743 / qualifier
 
Defining formula:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11743 / qualifier
 
xml-id: C18.S1.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11736 / rank
 
Normal rank
Property / Symbols used: Q11736 / qualifier
 
Defining formula:

N 𝑁 {\displaystyle{\displaystyle N}}

N
Property / Symbols used: Q11736 / qualifier
 
xml-id: C18.S1.XMD7.m1dec
Property / Symbols used
 
Property / Symbols used: Q11754 / rank
 
Normal rank
Property / Symbols used: Q11754 / qualifier
 
Defining formula:

δ 𝛿 {\displaystyle{\displaystyle\delta}}

\delta
Property / Symbols used: Q11754 / qualifier
 
xml-id: C18.S1.XMD8.m1dec

Latest revision as of 01:43, 2 January 2020

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English
DLMF:18.26.E3
No description defined

    Statements

    Defining formula
    R n ⁡ ( y ⁢ ( y + γ + δ + 1 ) ; α , β , γ , δ ) = F 3 4 ⁡ ( - n , n + α + β + 1 , - y , y + γ + δ + 1 α + 1 , β + δ + 1 , γ + 1 ; 1 ) , Racah-polynomial-R 𝑛 𝑦 𝑦 𝛾 𝛿 1 𝛼 𝛽 𝛾 𝛿 Gauss-hypergeometric-pFq 4 3 𝑛 𝑛 𝛼 𝛽 1 𝑦 𝑦 𝛾 𝛿 1 𝛼 1 𝛽 𝛿 1 𝛾 1 1 {\displaystyle{\displaystyle R_{n}\left(y(y+\gamma+\delta+1);\alpha,\beta,% \gamma,\delta\right)={{}_{4}F_{3}}\left({-n,n+\alpha+\beta+1,-y,y+\gamma+% \delta+1\atop\alpha+1,\beta+\delta+1,\gamma+1};1\right),}}
    0 references
    DLMF id
    DLMF:18.26.E3
    0 references
    constraint
    n = 0 , 1 , … , N 𝑛 0 1 … 𝑁 {\displaystyle{\displaystyle n=0,1,\dots,N}}
    0 references
    Symbols used
    Q11125
    Defining formula
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; z ) Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
    xml-id
    C16.S2.m1abdec
    0 references
    Q11785
    Defining formula
    R n ⁡ ( x ; α , β , γ , ) Racah-polynomial-R 𝑛 𝑥 𝛼 𝛽 𝛾 {\displaystyle{\displaystyle R_{\NVar{n}}\left(\NVar{x};\NVar{\alpha},\NVar{% \beta},\NVar{\gamma},\right)\)\@add@PDF@RDFa@triples\end{document}}}
    xml-id
    C18.S25.T1.t1.r4.m2adec
    0 references
    Q11743
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C18.S1.XMD1.m1bdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1bdec
    0 references
    Q11736
    Defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C18.S1.XMD7.m1dec
    0 references
    Q11754
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C18.S1.XMD8.m1dec
    0 references
     
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