Continuous ranking of zeros of special functions
Continuous ranking of zeros of special functions
复制标题
特殊函数零点的连续排序
DOI：
10.1016/j.jmaa.2008.01.082
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发表时间：
2008
影响因子：
1.3
通讯作者：
M. E. Muldoon
中科院分区：
文献类型：
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作者：
M. E. Muldoon
我们重新审视并继续J. Vosmansky [J. Vosmanskyp，Zeros of solutions of linear differential equations as continuous functions of the parameter k，in：J. Wiener，J.K.黑尔（编辑），偏微分方程，会议论文集，爱丁堡，德克萨斯州，1991年，在：皮特曼研究笔记数学系列，第273卷，1992年，第273页。[253-257]从二阶线性微分方程变换理论的观点讨论某些特殊函数的零点的连续排列的概念。这导致结果较高的单调性，这样的零相对于秩和评价的一些定积分。其应用是Airy，Bessel和Hermite函数。
We reexamine and continue the work of J. Vosmansky [J. Vosmanský, Zeros of solutions of linear differential equations as continuous functions of the parameter k, in: J. Wiener, J.K. Hale (Eds.), Partial Differential Equations, Proceedings of Conference, Edinburg, TX, 1991, in: Pitman Res. Notes Math. Ser., vol. 273, 1992, pp. 253–257] on the concept of continuous ranking of zeros of certain special functions from the point of view of the transformation theory of second-order linear differential equations. This leads to results on higher monotonicity of such zeros with respect to the rank and to the evaluation of some definite integrals. The applications are to Airy, Bessel and Hermite functions.