Electronic International Standard Serial Number (EISSN)
1660-5454
abstract
Let {Sn}n0 be the sequence of orthogonal polynomials with respect to the Laguerre–Sobolev inner product
f, gS = +∞ 0 f(x)g(x)xαe −xdx +N j=1 dj k=0 λj,kf(k)(cj)g(k)(cj), where λj,k 0, α > −1 and ci ∈ (−∞, 0) for i = 1, 2, . . . , N. We provide a formula that relates the Laguerre–Sobolev polynomials Sn to the classical Laguerre polynomials. We find the ladder operators for the polynomial sequence {Sn}n0 and a second-order differential equation with polynomial coefficients for {Sn}n0. We establish a sufficient condition for an electrostatic model of the zeros of orthogonal Laguerre–Sobolev polynomials. Some examples are given where this condition is either satisfied or not.
Classification
subjects
Mathematics
keywords
laguerre polynomials; sobolev orthogonality; second-order differential equation; electrostatic model