Convexity of the zeros of some orthogonal polynomials and related functions
Convexity of the zeros of some orthogonal polynomials and related functions
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一些正交多项式及相关函数的零点的凸性
DOI：
10.1016/j.cam.2009.02.045
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
F. Toókos
中科院分区：
文献类型：
--
作者：
K. Jordaan;F. Toókos
研究了由Sturm凸性定理导出的一些特殊函数零点的凸性。我们证明结果的凸性的拉盖尔，雅可比和超球面多项式的零点，以及与它们相关的功能，使用变换下的零点保持不变的间隔。我们给出了在几种情况下，连续零之间的距离的上限和下限。
We study convexity properties of the zeros of some special functions that follow from the convexity theorem of Sturm. We prove results on the intervals of convexity for the zeros of Laguerre, Jacobi and ultraspherical polynomials, as well as functions related to them, using transformations under which the zeros remain unchanged. We give upper as well as lower bounds for the distance between consecutive zeros in several cases.