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arXiv · 1705.01190

Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions

T. M. Dunster·A. Gil·J. Segura
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Abstract

Uniform asymptotic expansions involving exponential and Airy functions are obtained for Laguerre polynomials $L_{n}^{(\alpha)}(x)$, as well as complementary confluent hypergeometric functions. The expansions are valid for $n$ large and $\alpha$ small or large, uniformly for unbounded real and complex values of $x$. The new expansions extend the range of computability of $L_n^{(\alpha)}(x)$ compared to previous expansions, in particular with respect to higher terms and large values of $\alpha$. Numerical evidence of their accuracy for real and complex values of $x$ is provided.

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BibTeXRIS

T. M. Dunster, A. Gil, J. Segura. 2017-05-02. Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions. https://arxiv.org/abs/1705.01190

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