Interlacing and asymptotic properties of Stieltjes polynomials

Details Interlacing and asymptotic properties of Stieltjes polynomials Interlacing and asymptotic properties of Stieltjes polynomials

2009-03-03

arxiv.org/abs/0903.0644v1

Mathematics

Classical Analysis and ODEs

13 pages, 1 figure

Scientific paper

Polynomial solutions to the generalized Lam\'e equation, the \textit{Stieltjes polynomials}, and the associated \textit{Van Vleck polynomials} have been studied since the 1830's, beginning with Lam\'e in his studies of the Laplace equation on an ellipsoid, and in an ever widening variety of applications since. In this paper we show how the zeros of Stieltjes polynomials are distributed and present two new interlacing theorems. We arrange the Stieltjes polynomials according to their Van Vleck zeros and show, firstly, that the zeros of successive Stieltjes polynomials of the same degree interlace, and secondly, that the zeros of Stieltjes polynomials of successive degrees interlace. We use these results to deduce new asymptotic properties of Stieltjes and Van Vleck polynomials. We also show that no sequence of Stieltjes polynomials is orthogonal.

Affiliated with

Also associated with

No associations

Rating

Interlacing and asymptotic properties of Stieltjes 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 Interlacing and asymptotic properties of Stieltjes polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Interlacing and asymptotic properties of Stieltjes polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-368362