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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 thedegree \lambda -> \infty, apply the results to the case z \in (-1,1), andestablish the connection of these results to asymptotic Bessel-functionapproximations of the functions for z\rightarrow \pm 1.

Complex asymptotics in\ lambda for the Gegenbauer functions C_\lambda^\alpha(z) and D_\lambda^\alpha(z) with z\in(-1,1)