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DLMF:16.11.E5 - MaRDI portal
Statements
e
k
,
m
=
∑
j
=
1
q
+
1
(
1
-
ν
-
κ
b
j
+
m
)
κ
+
k
-
m
(
∏
ℓ
=
1
p
(
a
ℓ
-
b
j
)
/
∏
ℓ
=
1
ℓ
≠
j
q
+
1
(
b
ℓ
-
b
j
)
)
,
subscript
𝑒
𝑘
𝑚
superscript
subscript
𝑗
1
𝑞
1
Pochhammer
1
𝜈
𝜅
subscript
𝑏
𝑗
𝑚
𝜅
𝑘
𝑚
superscript
subscript
product
ℓ
1
𝑝
subscript
𝑎
ℓ
subscript
𝑏
𝑗
superscript
subscript
product
ℓ
1
ℓ
𝑗
𝑞
1
subscript
𝑏
ℓ
subscript
𝑏
𝑗
{\displaystyle{\displaystyle e_{k,m}=\sum_{j=1}^{q+1}{\left(1-\nu-\kappa b_{j}%
+m\right)_{\kappa+k-m}}\left({\textstyle\ifrac{\prod\limits_{\ell=1}^{p}(a_{%
\ell}-b_{j})}{\prod\limits_{\begin{subarray}{c}\ell=1\\
\ell\neq j\end{subarray}}^{q+1}(b_{\ell}-b_{j})}}\right),}}
(
a
)
n
Pochhammer
𝑎
𝑛
{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
p
𝑝
{\displaystyle{\displaystyle p}}
q
𝑞
{\displaystyle{\displaystyle q}}
a
,
a
1
,
…
,
a
p
𝑎
subscript
𝑎
1
…
subscript
𝑎
𝑝
{\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}
b
,
b
1
,
…
,
b
q
𝑏
subscript
𝑏
1
…
subscript
𝑏
𝑞
{\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}
κ
𝜅
{\displaystyle{\displaystyle\kappa}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers