A conjecture on Exceptional Orthogonal Polynomials

Details A conjecture on Exceptional Orthogonal Polynomials A conjecture on Exceptional Orthogonal Polynomials

2012-03-30

arxiv.org/abs/1203.6857v1

Physics

Mathematical Physics

Scientific paper

Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and Jacobi. They also generalize the family of CPRS orthogonal polynomials. We formulate the following conjecture: every exceptional orthogonal polynomial system is related to a classical system by a Darboux-Crum transformation. We give a proof of this conjecture for codimension 2 exceptional orthogonal polynomials (X2-OPs). As a by-product of this analysis, we prove a Bochner-type theorem classifying all possible X2-OPS. The classification includes all cases known to date plus some new examples of X2-Laguerre and X2-Jacobi polynomials.

Affiliated with

Also associated with

No associations

Rating

A conjecture on Exceptional Orthogonal Polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A conjecture on Exceptional Orthogonal Polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A conjecture on Exceptional Orthogonal Polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-64984