How do you compute the convolution of $n$ functions?

Question

I know that the convolution of two functions $f_1(x)$ and $f_2(x)$ is defined as $\int_{-\infty}^{\infty} f_1(z-t)f_2(t)dt$. My stochastic script states that the density function of the sum of random variables is the convolution of their density functions. Of course, I could compute this pieceswise, e.g. $Z=x_1+x_2+x_3+x_4$ where $x_i$ is a random variable with density function $f_i$. Then the density function of $Z$ is given by $f_1 * f_2*f_3*f_4$ and one can calculate this by first computing $f_{12}=f_1*f_2$ and $f_{34}=f_3*f_4$ and then $f_z=f_{12}*f_{34}$. But does there exist a description closed description of $f_z$, something like $f_z=\int f_1(x-t_1)f_2(x-t_2)f_3(x-t_3)f_4(x-t_4)dt_1 dt_2 dt_3 dt_4$?