# Convolute two independent general gamma distribution functions

I am trying to create a variable by adding two independent general Gamma probability functions $X$ and $Y$ so that $Z = X + Y$. Both functions have different parameters a and b.

$f(x) = b_1 \cdot x^{a_1-1} \cdot \frac{\exp(-b_1\cdot x)}{\Gamma(a_1)}$ and $g(y) = b_2 \cdot y^{a_2-1} \cdot \frac{\exp(-b_2\cdot y)}{\Gamma(a_2)}$

So far I have I have only been able to successfully convolute $X$ and $Y$ for the case when $b_1 = b_2$. I would appreciate if someone could give me some guidance as to how to accomplish this task.