RT Journal Article
T1 Differential properties of Jacobi-Sobolev polynomials and electrostatic interpretation
A1 Pijeira Cabrera, Héctor Esteban
A1 Quintero Roba, Javier Alejandro
A1 Toribio Milane, Juan
AB We study the sequence of monic polynomials {S-n}n >= 0, orthogonal with respect to the JacobiSobolev inner product < f,g > s = integral(1)(-1) f (x)g(x) d mu(alpha,beta)(x) + Sigma (N)(dj)(j=1) lambda(j,k),f(k) (c(j))g((k))(cj), where N, d(j) is an element of Z(+), lambda(j,k) >= 0, d mu(alpha,beta)(x) = (1-x)(alpha)(1 + x)beta (dx), alpha, beta > -1, and c(j) is an element of R backslash(-1, 1). A connection formula that relates the Sobolev polynomials Sn with the Jacobi polynomials is provided, as well as the ladder differential operators for the sequence {S-n}(n >= 0) and a second-order differential equation with a polynomial coefficient that they satisfied. We give sufficient conditions under which the zeros of a wide class of Jacobi-Sobolev polynomials can be interpreted as the solution of an electrostatic equilibrium problem of n unit charges moving in the presence of a logarithmic potential. Several examples are presented to illustrate this interpretation.
PB MDPI
SN 2227-7390
YR 2023
FD 2023-08-06
LK https://hdl.handle.net/10016/38400
UL https://hdl.handle.net/10016/38400
LA eng
NO This article belongs to the Special Issue Orthogonal Polynomials and Special Functions: Recent Trends and Their Applications.
NO The research of J. Toribio-Milane was partially supported by Fondo Nacional de Innovación y Desarrollo Científico y Tecnológico (FONDOCYT), Dominican Republic, under grant 2020-2021-1D1-137.
DS e-Archivo
RD 17 jul. 2024