Complex asymptotics in\ lambda for the Gegenbauer functions C_λ^α(z) and D_λ^α(z) with z\in(-1,1)
arXiv:1911.04905
Abstract
We derive asymptotic results for the Gegenbauer functions C_λ^α(z) and D_λ^α(z) of the first and second kind for complex z and the degree λ-> \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.
14 pages