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DLMF:16.14#Ex3

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Formula:5952
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MaRDI QIDQ5952

  • 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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