Can a logarithm function with two variable be expressed as a Meijer-G function?

Question

Let {x},{y}>0 and {a},{b}>0. can the function log(1+ax+by) be expressed as a Meijer-G function?

Answer 1

This is meant to be an outline of an answer. The details of arguments for the Meijer-G functions still need to be filled in:

z[x_, y_] = a1 x + b2 y;
\[Alpha] = Evaluate@MeijerGReduce[Log[1 + z[x, y]], z[x, y]];
\[Beta] = MeijerG[{{}, {}}, {{}, {}}, a2 x];
\[Gamma] = MeijerG[{{}, {}}, {{}, {}}, b2 y];
f = \[Alpha] \[Beta] \[Gamma];
Integrate[f, {x, 0, \[Infinity]}, {y, 0, \[Infinity]}]