论文标题
Charlier多项式的渐近根分布，具有较大的负参数
Asymptotic root distribution of Charlier polynomials with large negative parameter
论文作者
论文摘要
我们根据索引线性地分析了具有负参数的Charlier多项式的根的渐近分布。复杂平面中的曲线上的根簇。我们确定这些曲线的隐式方程，并推断出这些曲线支持的根分布的限制密度。该证明是基于确定特定区域中限制性cauchy变换的确定，并仔细应用了鞍点方法。获得的结果代表了一个更普遍的开放问题的可解决示例。
We analyze the asymptotic distribution of roots of Charlier polynomials with negative parameter depending linearly on the index. The roots cluster on curves in the complex plane. We determine implicit equations for these curves and deduce the limiting density of the root distribution supported on these curves. The proof is based on a determination of the limiting Cauchy transform in a specific region and a careful application of the saddle point method. The obtained result represents a solvable example of a more general open problem.
