I have a problem that involves the H-function of several variables, and I have noticed that the implementation of such function when the number of variables are relatively high (greater than 5) must be done through some integral representation of the H-function.
My question is what is an integral representation for the Fox H function of several variables?
According to Wikipedia:
The Mellin-Barnes integral representation is $$ H_{p,q}^{\,m,n} \!\left[ z \left| \begin{matrix} ( a_1 , A_1 ) & ( a_2 , A_2 ) & \ldots & ( a_p , A_p ) \\ ( b_1 , B_1 ) & ( b_2 , B_2 ) & \ldots & ( b_q , B_q ) \end{matrix} \right. \right] = \\\frac{1}{2\pi i}\int_L \frac {(\prod_{j=1}^m\Gamma(b_j+B_js))(\prod_{j=1}^n\Gamma(1-a_j-A_js))} {(\prod_{j=m+1}^q\Gamma(1-b_j-B_js))(\prod_{j=n+1}^p\Gamma(a_j+A_js))} z^{-s} \, ds $$ where $L$ is a certain contour separating the poles of the two factors in the numerator.