کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4640548 | 1341278 | 2010 | 12 صفحه PDF | دانلود رایگان |
In a series of seminal papers, Thomas J. Stieltjes (1856–1894) gave an elegant electrostatic interpretation for the zeros of classical families of orthogonal polynomials, such as Jacobi, Hermite and Laguerre polynomials. More generally, he extended this approach to the zeros of polynomial solutions of certain second-order linear differential equations (Lamé equations), the so-called Heine–Stieltjes polynomials.In this paper, a class of electrostatic equilibrium problems in RR, where the free unit charges x1,…,xn∈Rx1,…,xn∈R are in presence of a finite family of “attractors” (i.e., negative charges) z1,…,zm∈C∖Rz1,…,zm∈C∖R, is considered and its connection with certain class of Lamé-type equations is shown. In addition, we study the situation when both n→∞n→∞ and m→∞m→∞, by analyzing the corresponding (continuous) equilibrium problem in presence of a certain class of external fields.
Journal: Journal of Computational and Applied Mathematics - Volume 235, Issue 4, 15 December 2010, Pages 1065–1076