# Uniform asymptotic expansions for Gegenbauer polynomials and related functions via differential equations having a simple pole

@inproceedings{Dunster2022UniformAE, title={Uniform asymptotic expansions for Gegenbauer polynomials and related functions via differential equations having a simple pole}, author={T. Mark Dunster}, year={2022} }

. Asymptotic expansions are derived for Gegenbauer (ultraspherical) polynomials for large order n that are uniformly valid for unbounded complex values of the argument z , including the real interval 0 ≤ z ≤ 1 in which the zeros are located. The approximations are derived from the diﬀerential equation satisﬁed by these polynomials, and other independent solutions are also considered. For large n this equation is characterized by having a simple pole, and expansions valid at this singularity…

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