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According to http://en.wikipedia.org/wiki/Appell_series#Integral_representations and http://en.wikipedia.org/wiki/Lauricella_hypergeometric_series#Integral_representation_of_FD, it is known that $F_1(a,b_1,b_2,c;x,y)$ and $F_D^{(n)}(a,b_1,\ldots,b_n,c;x_1,\ldots,x_n)$ have the single integral forms that

$F_1(a,b_1,b_2,c;x,y)=\dfrac{\Gamma(c)}{\Gamma(a)\Gamma(c-a)}\int_0^1t^{a-1}(1-t)^{c-a-1}(1-xt)^{-b_1}(1-yt)^{-b_2}~dt$ , where $\text{Re}(c)>\text{Re}(a)>0$

$F_D^{(n)}(a,b_1,\ldots,b_n,c;x_1,\ldots,x_n)=\dfrac{\Gamma(c)}{\Gamma(a)\Gamma(c-a)}\int_0^1t^{a-1}(1-t)^{c-a-1}(1-x_1t)^{-b_1}\cdots(1-x_nt)^{-b_n}~dt$ , where $\text{Re}(c)>\text{Re}(a)>0$

But how about $F_2(a,b_1,b_2,c;x,y)$ , $F_3(a,b_1,b_2,c;x,y)$ , $F_4(a,b_1,b_2,c;x,y)$ , $F_A^{(n)}(a,b_1,\ldots,b_n,c;x_1,\ldots,x_n)$ , $F_B^{(n)}(a,b_1,\ldots,b_n,c;x_1,\ldots,x_n)$ and $F_C^{(n)}(a,b_1,\ldots,b_n,c;x_1,\ldots,x_n)$ ? Are they have the single integral forms similar to $F_1(a,b_1,b_2,c;x,y)$ and $F_D^{(n)}(a,b_1,\ldots,b_n,c;x_1,\ldots,x_n)$ ?

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