Vtyjkyuk

I would like to run the following function :

"The generalized upper incomplete Fox’s H function"

given by

$$
largeH_m,n^p,qleft( z left| beginarraycc (a_1,alpha_1,A_1)cdots (a_p,alpha_p,A_p) \ (a_1,alpha_1,A_1)cdots (b_p,beta_p,B_p) endarray right. right).
$$

$$
frac12pi joint_L frac
prod_i=1^mGamma(b_i+beta_is,B_i)prod_i=1^nGamma(1-a_i-alpha_is,A_i)
prod_i=n+1^pGamma(a_i+alpha_is,A_i) prod_i=m+1^qGamma(1-b_i-beta_is,B_i)
z^-sds.
$$
I found a program, for this function. My problem is in the contour integration path in the complex $s$-plane running from $R-iW$ to $R+iW$.

I do not now how I chose $R$. ?

The author of program said that:

The parameters, $R$ and $W$, are determined according to convergence
region such that the contour integration path in the complex $s$-plane
running from $R-iW$ to $R+iW$,

$i=sqrt(-1)$

$W$ goes to $infty$ [i.e., it may be chosen as 100]

The value of $Rin R$ is an arbitrary real number chosen between the points $s =((-b_j-k))⁄beta_j$ for $1≤j≤m$ and $k=0,1,2,…$ and the points $s = ((1-a_i+k))⁄alpha_i$ for $1≤i≤n$ and $k=0,1,2,…$ lie to the left and right of the chosen contour, respectively.*)

Also i found in other book the following explanation, however hi dose not use the same notation in the program, hi define as follow

$$
frac12pi joint_L frac
prod_i=1^mGamma(b_i+B_is)prod_i=1^nGamma(1-a_i-A_is)
prod_i=n+1^pGamma(a_i+A_is) prod_i=m+1^qGamma(1-b_i-B_is)
z^-sds.
$$
but my be his explanation it help.
$L$ is a suitable contour separating the poles

$P_jv=-fracb_j+vB_j$, $j=1,2,cdots,m; v=0,1,cdots$

of the gamma functions $Gamma(b_j+sB_j)$ from the poles

$P_tk=-frac1-a_t+kA_t$, $t=1,2,cdots,n; k=0,1,cdots$

of the gamma functions $Gamma(1-a_t+sB_t)$, that is

$$A_t(b_j+v)=B_j(a_t-1-k).$$

So for given $a_i,alpha_i,A_i$ and $b_i,beta_i,B_i$, how i can chose $R$.

Thanks.