  In planar slow-fast systems, fractal analysis of (bounded) sequences in
$\mathbb R$ has proved important for detection of the first non-zero Lyapunov
quantity in singular Hopf bifurcations, determination of the maximum number of
limit cycles produced by slow-fast cycles, defined in the finite plane, etc.
One uses the notion of Minkowski dimension of sequences generated by slow
relation function. Following a similar approach, together with
Poincar\'{e}--Lyapunov compactification, in this paper we focus on a fractal
analysis near infinity of the slow-fast generalized Li\'{e}nard equations $\dot
x=y-\sum_{k=0}^{n+1} B_kx^k,\ \dot y=-\epsilon\sum_{k=0}^{m}A_kx^k$. We extend
the definition of the Minkowski dimension to unbounded sequences. This helps us
better understand the fractal nature of slow-fast cycles that are detected
inside the slow-fast Li\'{e}nard equations and contain a part at infinity.
