2008/12/03 by W. N. Everitt, Everitt, W. N. · 1 citation
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum Mechanics and Non-Hermitian Physics #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.0812.0728
This note supplements the work of Gomez-Ullate, Kamran and Milson on the X_(1)-Jacobi polynomials which are orthogonal in a weighted Hilbert function space on the the interval (-1,+1) of the real line. These polynomials are generated by a second-order ordinary linear differential equation with a spectral parameter. Some additional information on the Sturm-Liouville form of this equation is given in this note, together with details of the singular differential operators generated in the weighted Hilbert function space. In particular, structured boundary conditions are given to determine the special self-adjoint operator, whose discrete spectrum and associated eigenvectors yield the X_(1)-Jacobi polynomials.