Zeros of linear combinations of Laguerre polynomials from different sequences

Details Zeros of linear combinations of Laguerre polynomials from different sequences Zeros of linear combinations of Laguerre polynomials from different sequences

2008-12-03

arxiv.org/abs/0812.0730v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We study interlacing properties of the zeros of two types of linear combinations of Laguerre polynomials with different parameters, namely $R_n=L_n^{\alpha}+aL_{n}^{\alpha'}$ and $S_n=L_n^{\alpha}+bL_{n-1}^{\alpha'}$. Proofs and numerical counterexamples are given in situations where the zeros of $R_n$, and $S_n$, respectively, interlace (or do not in general) with the zeros of $L_k^{\alpha}$, $L_k^{\alpha'}$, $k=n$ or $n-1$. The results we prove hold for continuous, as well as integral, shifts of the parameter $\alpha$.

Affiliated with

Also associated with

No associations

Rating

Zeros of linear combinations of Laguerre polynomials from different sequences 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 Zeros of linear combinations of Laguerre polynomials from different sequences, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Zeros of linear combinations of Laguerre polynomials from different sequences will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-625401