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

Loyal Durand

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arXiv · 1911.04905

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

Loyal Durand

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Abstract

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.

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BibTeX RIS

Loyal Durand. 2019-11-11. Complex asymptotics in\ lambda for the Gegenbauer functions C_\lambda^\alpha(z) and D_\lambda^\alpha(z) with z\in(-1,1). https://arxiv.org/abs/1911.04905

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