Integration problem

Question

I'm trying to solve this integral including the MeijerG function using Mathematica :

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

But, it keeps giving me the same integral I write as follows:

Integrate[
 E^(-b r^(-a/2) x^(l/k) - b r^(-a/2) (-x + z)^(l/k))
   x^(-1 + (a b)/2) (-x + z)^(-1 + (a b)/2), {x, 0, z}]

What can i do to get the output of this integration??

Answer 1

With

$Version

(* "10.4.1 for Microsoft Windows (64-bit) (April 11, 2016)" *)

the integral does have a symbolic solution for k == l (and the spurious comma deleted from just before the final bracket).

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

(* ConditionalExpression[(E^(-b r^(-a/2) z) z^(-1 + a b) Gamma[(a b)/2]^2)/Gamma[a b], 
   Re[a b] > 0 && Re[z] > 0 && Im[z] == 0] *)

This solution is not as general as that requested but may still be of use.