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Statements
P
j
=
Γ
(
α
+
j
)
Γ
(
1
-
γ
+
α
+
j
)
Γ
(
1
+
α
-
β
+
ϵ
+
2
j
)
z
-
α
-
j
F
1
2
(
α
+
j
,
1
-
γ
+
α
+
j
1
+
α
-
β
+
ϵ
+
2
j
;
1
z
)
,
subscript
𝑃
𝑗
Euler-Gamma
𝛼
𝑗
Euler-Gamma
1
𝛾
𝛼
𝑗
Euler-Gamma
1
𝛼
𝛽
italic-ϵ
2
𝑗
superscript
𝑧
𝛼
𝑗
Gauss-hypergeometric-F-as-2F1
𝛼
𝑗
1
𝛾
𝛼
𝑗
1
𝛼
𝛽
italic-ϵ
2
𝑗
1
𝑧
{\displaystyle{\displaystyle P_{j}=\frac{\Gamma\left(\alpha+j\right)\Gamma%
\left(1-\gamma+\alpha+j\right)}{\Gamma\left(1+\alpha-\beta+\epsilon+2j\right)}%
z^{-\alpha-j}\*{{}_{2}F_{1}}\left({\alpha+j,1-\gamma+\alpha+j\atop 1+\alpha-%
\beta+\epsilon+2j};\frac{1}{z}\right),}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
F
1
2
(
a
,
b
;
c
;
z
)
Gauss-hypergeometric-F-as-2F1
𝑎
𝑏
𝑐
𝑧
{\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};%
\NVar{z}\right)}}
z
𝑧
{\displaystyle{\displaystyle z}}
γ
𝛾
{\displaystyle{\displaystyle\gamma}}
ϵ
italic-ϵ
{\displaystyle{\displaystyle\epsilon}}
j
𝑗
{\displaystyle{\displaystyle j}}
α
𝛼
{\displaystyle{\displaystyle\alpha}}
β
𝛽
{\displaystyle{\displaystyle\beta}}
P
j
subscript
𝑃
𝑗
{\displaystyle{\displaystyle P_{j}}}
