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Open AccessArticle

Complex Asymptotics in λ for the Gegenbauer Functions Cλα(z) and Dλα(z) with z∈(-1,1)

Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA
Symmetry 2019, 11(12), 1465; https://doi.org/10.3390/sym11121465
Received: 9 November 2019 / Revised: 21 November 2019 / Accepted: 22 November 2019 / Published: 1 December 2019
(This article belongs to the Special Issue Symmetry in Special Functions and Orthogonal Polynomials)
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 | , apply the results to the case z ( - 1 , 1 ) , and establish the connection of these results to asymptotic Bessel-function approximations of the functions for z ± 1 .
Keywords: Gegenbauer functions; asymptotics Gegenbauer functions; asymptotics
MDPI and ACS Style

Durand, L. Complex Asymptotics in λ for the Gegenbauer Functions Cλα(z) and Dλα(z) with z∈(-1,1). Symmetry 2019, 11, 1465.

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