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We find the large number asymptotic expansion of the Gegenbauer polynomials \(C_{n}^{\lambda } \left( {\cos \theta } \right)\) uniform in 0 ≤ θ ≤ π by further developing our method that reduces the procedure to regular perturbations. The method and result is compared with the ones published earlier.

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Uniform Asymptotic Expansion for Gegenbauer Polynomials: New Approach

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  • 发表日期：

    2025年

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  • Leonid Bakaleinikov,
  • Alexander Silbergleit

摘要

We find the large number asymptotic expansion of the Gegenbauer polynomials \(C_{n}^{\lambda } \left( {\cos \theta } \right)\) uniform in 0 ≤ θ ≤ π by further developing our method that reduces the procedure to regular perturbations. The method and result is compared with the ones published earlier.