Note on the X_(1)-Laguerre orthogonal polynomials

Details Note on the X_(1)-Laguerre orthogonal polynomials Note on the X_(1)-Laguerre orthogonal polynomials

2008-11-21

arxiv.org/abs/0811.3559v2

Mathematics

Classical Analysis and ODEs

5 pages The wrong LaTeX file was uploaded in error

Scientific paper

This note supplements the work of Gomez-Ullate, Kamran and Milson on the X_(1)-Laguerre polynomials which are orthogonal in a weighted Hilbert function space on the positive half-line 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)-Laguerre polynomials.

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