  In this work a method for numerical computation of the Schl\"afli function
$f_n(x)$, for $x\in[n-1,n+1]$ and $n\geq4$ is presented. The computation is
based on the Chebyshev approximation of the function $q_{n}(x)$, which is
related to the Schl\"afli function and regular in the interval.
