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DLMF:18.26.E3 - MaRDI portal
Statements
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),}}
n
=
0
,
1
,
…
,
N
𝑛
0
1
…
𝑁
{\displaystyle{\displaystyle n=0,1,\dots,N}}
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)}}
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}}}
y
𝑦
{\displaystyle{\displaystyle y}}
n
𝑛
{\displaystyle{\displaystyle n}}
N
𝑁
{\displaystyle{\displaystyle N}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
Identifiers