Asymptotics of Sobolev orthogonal polynomials for coherent pairs of Jacobi type
The authors define a sequence of orthogonal polynomials with respect to the Sobolev inner product \[ (f,g)_S=\int f(x)g(x)d\psi_0(x)+\lambda\int f'(x)g'(x)d\psi_1(x) \] where \(\lambda\) and \(\{d\psi_0(x),d\psi_1(x)\}\) is a so-called coherent pair with at least one of the measures \(d\psi_0\) or \(\psi_1\) a Jacobi measure. The asymptotics of \(S_n(x)\) are investigated when \(n\to\infty\) and \(x\) fixed in a different interval.
scientific article; zbMATH DE number 1367891