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DLMF:16.14#Ex3
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Formula:5952
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MaRDI QID
Q5952
Label: DLMF:16.14#Ex3
Digital Library of Mathematical Functions ID
16.14#Ex3
x
(
1
-
x
)
∂
2
F
2
∂
x
2
-
x
y
∂
2
F
2
∂
x
∂
y
+
(
γ
-
(
α
+
β
+
1
)
x
)
∂
F
2
∂
x
-
β
y
∂
F
2
∂
y
-
α
β
F
2
=
0
,
𝑥
1
𝑥
partial-derivative
Appell-F-2
𝑥
2
𝑥
𝑦
Appell-F-2
2
𝑥
𝑦
𝛾
𝛼
𝛽
1
𝑥
partial-derivative
Appell-F-2
𝑥
𝛽
𝑦
partial-derivative
Appell-F-2
𝑦
𝛼
𝛽
Appell-F-2
0
{\displaystyle{\displaystyle x(1-x)\frac{{\partial}^{2}{F_{2}}}{{\partial x}^{% 2}}-xy\frac{{\partial}^{2}{F_{2}}}{\partial x\partial y}+\left(\gamma-(\alpha+% \beta+1)x\right)\frac{\partial{F_{2}}}{\partial x}-\beta y\frac{\partial{F_{2}% }}{\partial y}-\alpha\beta{F_{2}}=0,}}
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