  In this article, using the notion of group contraction, we obtain the
spherical functions of the strong Gelfand pair $(\mathrm{M}(n),\mathrm{SO}(n))$
as an appropriate limit of spherical functions of the strong Gelfand pair
$(\mathrm{SO}(n+1),\mathrm{SO}(n))$ and also of the strong Gelfand pair
$(\mathrm{SO}_0(n,1),\mathrm{SO}(n))$.
