Help with contour integral method for Fox-H function

Hello,

I am working on a research problem in wireless communications that requires numerically evaluating an equation containing the Fox-H function. Since direct evaluation is computationally intensive and continuously running, I am exploring the contour integral method for more efficient computation in Mathematica.

Could anyone provide guidance or sample Mathematica code for implementing the contour integral method to evaluate the Fox-H function? Any insights on numerical stability and efficient integration techniques would also be appreciated.

For simple cases with standard commands for example:

Dear Mariusz Iwaniuk,

I sincerely appreciate your response to my query regarding the Contour Integral Method for the Fox-H function in Mathematica. Your insights on handling simpler cases with standard commands were quite helpful.

In my current implementation, the Fox-H function is running in its traditional representation. I would like to inquire whether you have any recommendations for handling it efficiently in this form. I have attached my Mathematica file for reference. Your guidance would be highly valuable.

Thank you again for your time and expertise.

work.nb (8.03 KB)

One way is:

Regards M.I.

Contour Numeric method:

Regards M.I