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DLMF:16.14#Ex6 - MaRDI portal

DLMF:16.14#Ex6 (Q5955)

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DLMF:16.14#Ex6
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    DLMF defining formula
    y ⁢ ( 1 - y ) ⁢ ∂ 2 ⁡ F 3 ∂ ⁡ y 2 + x ⁢ ∂ 2 ⁡ F 3 ∂ ⁡ x ⁢ ∂ ⁡ y + ( γ - ( α ′ + β ′ + 1 ) ⁢ y ) ⁢ ∂ ⁡ F 3 ∂ ⁡ y - α ′ ⁢ β ′ ⁢ F 3 = 0 , 𝑦 1 𝑦 partial-derivative Appell-F-3 𝑦 2 𝑥 Appell-F-3 2 𝑥 𝑦 𝛾 superscript 𝛼 ′ superscript 𝛽 ′ 1 𝑦 partial-derivative Appell-F-3 𝑦 superscript 𝛼 ′ superscript 𝛽 ′ Appell-F-3 0 {\displaystyle{\displaystyle y(1-y)\frac{{\partial}^{2}{F_{3}}}{{\partial y}^{% 2}}+x\frac{{\partial}^{2}{F_{3}}}{\partial x\partial y}+\left(\gamma-(\alpha^{% \prime}+\beta^{\prime}+1)y\right)\frac{\partial{F_{3}}}{\partial y}-\alpha^{% \prime}\beta^{\prime}{F_{3}}=0,}}
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