• Corpus ID: 252439220

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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