Antonio J. Dur'an

activity

20242026

collaborators

7 papers

math.GM2026

Zeros of GKP sequences of polynomials

Antonio J. DurÃ¡n, Mario PÃ©rez, Juan L. Varona

Given two sequences $I ¨ = (I ¨ _{i})_{i \geq 1}$ and $I ¨ = (I ¨ _{i})_{i \geq 1}$ and numbers $a, b, c$ , we introduce the GKP sequence of polynomials $(p_{n})_{n}$ using the following recurrence formula…

math.CA2025

Using quasi-Darboux transformations to construct exceptional matrix polynomials

Ignacio Bono Parisi, Antonio J. DurÃ¡n, Ignacio N. ZurriÃ¡n

We introduce a couple of methods to construct exceptional matrix polynomials. One of them uses what we have called quasi-Darboux transformations. This seems to be a more powerful m…

math.CA2025

Zeros of linear combinations of Laguerre polynomials

Antonio J. DurÃ¡n

We study the number of real zeros of finite combinations of $K + 1$ consecutive normalized Laguerre polynomials of the form $$ q_n(x)=\sum_{j=0}^KÎ³_j\tilde L^Î±_{n-j}(x),\quad n\ge…

math.CA2025

Zeros of linear combinations of Hermite polynomials

Antonio J. DurÃ¡n

We study the number of real zeros of finite combinations of $K + 1$ consecutive normalized Hermite polynomials of the form $$ q_n(x)=\sum_{j=0}^KÎ³_j\tilde H_{n-j}(x),\quad n\ge K, $…

math.CA2025

Zeros of linear combinations of orthogonal polynomials

Antonio J. DurÃ¡n

Given a sequence of orthogonal polynomials $(p_{n})_{n}$ with respect to a positive measure in the real line, we study the real zeros of finite combinations of $K + 1$ consecutive orthog…

math.NT2024

Asymptotic for the rightmost zeros of Bell and Eulerian polynomials

Antonio J. DurÃ¡n

Write $I^¶_{m} (n)$ , $1 \leq m \leq n - 1$ , for the negative zeros of the $n$ -th Bell polynomial, ordered in decreasing size. In this paper, we prove the following asymptotic: for a positive…