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Statements
P
{
α
β
γ
a
1
b
1
c
1
z
a
2
b
2
c
2
}
=
(
z
-
α
z
-
γ
)
a
1
(
z
-
β
z
-
γ
)
b
1
P
{
0
1
∞
0
0
a
1
+
b
1
+
c
1
(
z
-
α
)
(
β
-
γ
)
(
z
-
γ
)
(
β
-
α
)
a
2
-
a
1
b
2
-
b
1
a
1
+
b
1
+
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
superscript
𝑧
𝛼
𝑧
𝛾
subscript
𝑎
1
superscript
𝑧
𝛽
𝑧
𝛾
subscript
𝑏
1
Riemann-P-symbol
0
1
absent
0
0
subscript
𝑎
1
subscript
𝑏
1
subscript
𝑐
1
𝑧
𝛼
𝛽
𝛾
𝑧
𝛾
𝛽
𝛼
subscript
𝑎
2
subscript
𝑎
1
subscript
𝑏
2
subscript
𝑏
1
subscript
𝑎
1
subscript
𝑏
1
subscript
𝑐
2
absent
{\displaystyle{\displaystyle P\begin{Bmatrix}\alpha&\beta&\gamma&\\
a_{1}&b_{1}&c_{1}&z\\
a_{2}&b_{2}&c_{2}&\end{Bmatrix}=\left(\frac{z-\alpha}{z-\gamma}\right)^{a_{1}}%
\left(\frac{z-\beta}{z-\gamma}\right)^{b_{1}}P\begin{Bmatrix}0&1&\infty&\\
0&0&a_{1}+b_{1}+c_{1}&\dfrac{(z-\alpha)(\beta-\gamma)}{(z-\gamma)(\beta-\alpha%
)}\\
a_{2}-a_{1}&b_{2}-b_{1}&a_{1}+b_{1}+c_{2}&\end{Bmatrix}.}}
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}}}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
b
𝑏
{\displaystyle{\displaystyle b}}
c
𝑐
{\displaystyle{\displaystyle c}}
α
𝛼
{\displaystyle{\displaystyle\alpha}}
β
𝛽
{\displaystyle{\displaystyle\beta}}
γ
𝛾
{\displaystyle{\displaystyle\gamma}}
Identifiers
