  We derive asymptotic results for the Gegenbauer functions C_\lambda^\alpha(z)
and D_\lambda^\alpha(z) of the first and second kind for complex z and the
degree \lambda -> \infty, apply the results to the case z \in (-1,1), and
establish the connection of these results to asymptotic Bessel-function
approximations of the functions for z\rightarrow \pm 1.
