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DLMF:16.14#Ex2 - MaRDI portal

DLMF:16.14#Ex2 (Q5951)

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DLMF:16.14#Ex2
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    DLMF defining formula
    y ⁢ ( 1 - y ) ⁢ ∂ 2 ⁡ F 1 ∂ ⁡ y 2 + x ⁢ ( 1 - y ) ⁢ ∂ 2 ⁡ F 1 ∂ ⁡ x ⁢ ∂ ⁡ y + ( γ - ( α + β ′ + 1 ) ⁢ y ) ⁢ ∂ ⁡ F 1 ∂ ⁡ y - β ′ ⁢ x ⁢ ∂ ⁡ F 1 ∂ ⁡ x - α ⁢ β ′ ⁢ F 1 = 0 , 𝑦 1 𝑦 partial-derivative Appell-F-1 𝑦 2 𝑥 1 𝑦 Appell-F-1 2 𝑥 𝑦 𝛾 𝛼 superscript 𝛽 ′ 1 𝑦 partial-derivative Appell-F-1 𝑦 superscript 𝛽 ′ 𝑥 partial-derivative Appell-F-1 𝑥 𝛼 superscript 𝛽 ′ Appell-F-1 0 {\displaystyle{\displaystyle y(1-y)\frac{{\partial}^{2}{F_{1}}}{{\partial y}^{% 2}}+x(1-y)\frac{{\partial}^{2}{F_{1}}}{\partial x\partial y}+\left(\gamma-(% \alpha+\beta^{\prime}+1)y\right)\frac{\partial{F_{1}}}{\partial y}-\beta^{% \prime}x\frac{\partial{F_{1}}}{\partial x}-\alpha\beta^{\prime}{F_{1}}=0,}}
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