Gold 65

Appell series

Gold ID: 65
Link: https://sigir21.wmflabs.org/wiki/Appell_series#math.117.19
Formula: $x (1 - x) \frac{\partial^{2} F_{1} (x, y)}{\partial x^{2}} + y (1 - x) \frac{\partial^{2} F_{1} (x, y)}{\partial x \partial y} + [c - (a + b_{1} + 1) x] \frac{\partial F_{1} (x, y)}{\partial x} - b_{1} y \frac{\partial F_{1} (x, y)}{\partial y} - a b_{1} F_{1} (x, y) = 0$
TeX Source: x(1-x) \frac {\partial^2F_1(x,y)} {\partial x^2} + y(1-x) \frac {\partial^2F_1(x,y)} {\partial x \partial y} + [c - (a+b_1+1) x] \frac {\partial F_1(x,y)} {\partial x} - b_1 y \frac {\partial F_1(x,y)} {\partial y} - a b_1 F_1(x,y) = 0

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
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Translation: x(1 - x) \deriv [2]{F_1(x , y)}{x} + y(1 - x) \frac {\partial^2F_1(x,y)} {\partial x \partial y} + [c -(a + b_1 + 1) x] \deriv [1]{F_1(x , y)}{x} - b_1 y \deriv [1]{F_1(x , y)}{y} - a b_1 F_1(x , y) = 0
Expected (Gold Entry): x(1-x) \deriv[2]{\AppellF{1}@{a}{b_1}{b_2}{\gamma}{x}{y}}{x} + y(1-x) \frac{\pdiff[2]{\AppellF{1}@{a}{b_1}{b_2}{\gamma}{x}{y}}}{\pdiff{x}\pdiff{y}} + [c - (a+b_1+1) x] \deriv[1]{\AppellF{1}@{a}{b_1}{b_2}{\gamma}{x}{y}}{x} - b_1 y \deriv[1]{\AppellF{1}@{a}{b_1}{b_2}{\gamma}{x}{y}}{y} - a b_1 \AppellF{1}@{a}{b_1}{b_2}{\gamma}{x}{y} = 0

Translation
Expected (Gold Entry): x*(1-x) * D[AppellF[a, Subscript[b, 1], Subscript[b, 2], \[Gamma], x, y], {x,2}] + y*(1-x) * D[AppellF[a, Subscript[b, 1], Subscript[b, 2], \[Gamma], x, y], x, y] + (c - (a+Subscript[b, 1]+1)*x) * D[AppellF[a, Subscript[b, 1], Subscript[b, 2], \[Gamma], x, y], x] - Subscript[b,1] * y * D[AppellF[a, Subscript[b, 1], Subscript[b, 2], \[Gamma], x, y], y] - a*Subscript[b,1]*AppellF[a, Subscript[b, 1], Subscript[b, 2], \[Gamma], x, y] == 0