Multiplication of special functions

Question

Can anyone please give me the answer of this multiplication in the terms of another MeijerG function?

MeijerG[{{}, {}}, {{0}, {}}, (b*x^(a/2))/r^(a/2)]*
  (z - x)^((a*b/2) - 1)*
  MeijerG[{{}, {}}, {{0}, {}}, (b*(z - x)^(a/2))/r^(a/2)]

where a > 0 and b > 0.5.

Answer 1

This is not an answer, but a request for more information that is too long for a comment.

When I evaluate your expression in V10.4.1, I get

E^(-b r^(-a/2) x^(a/2) - b r^(-a/2) (-x + z)^(a/2)) (-x + z)^(-1 + (a b)/2)

Why is this not a good result? Why do you insist Mathematica return a result in the form of MeijerG[...]?

Note that the documentation of MeijerG says

In many special cases, MeijerG is automatically converted to other functions.

Answer 2

If you are using version 9.0 you may only need to update to version 9.0.1

Using version 9.0.1.0 on a Mac

$Version

(*  "9.0 for Mac OS X x86 (64-bit) (January 24, 2013)"  *)

expr = MeijerG[{{}, {}}, {{0}, {}}, (b*x^(a/2))/
    r^(a/2)]*(z - x)^((a*b/2) - 1)*
  MeijerG[{{}, {}}, {{0}, {}}, (b*(z - x)^(a/2))/r^(a/2)]

(*  E^(((-b)*x^(a/2))/r^(a/2) - 
        (b*(-x + z)^(a/2))/r^(a/2))*
   (-x + z)^(-1 + (a*b)/2)  *)

expr // Simplify

(*  (-x + z)^(-1 + (a*b)/2)/
   E^((b*(x^(a/2) + (-x + z)^
                (a/2)))/r^(a/2))  *)