50 citations · 51 across the 8 of their papers we have counts for
9 papers
Zeros of GKP sequences of polynomials
Antonio J. Durán, Mario Pérez, Juan L. Varona
Given two sequences and and numbers , we introduce the GKP sequence of polynomials using the following recurrence formula: $p…
Using quasi-Darboux transformations to construct exceptional matrix polynomials
Ignacio Bono Parisi, Antonio J. Durán, Ignacio N. Zurrián
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…
Zeros of linear combinations of Laguerre polynomials
Antonio J. Durán
We study the number of real zeros of finite combinations of consecutive normalized Laguerre polynomials of the form $$ q_n(x)=\sum_{j=0}^Kγ_j\tilde L^α_{n-j}(x),\quad n\ge K,…
Zeros of linear combinations of Hermite polynomials
Antonio J. Durán
We study the number of real zeros of finite combinations of consecutive normalized Hermite polynomials of the form …
Zeros of linear combinations of orthogonal polynomials
Antonio J. Durán
Given a sequence of orthogonal polynomials with respect to a positive measure in the real line, we study the real zeros of finite combinations of consecutive orthog…
Brenke polynomials with real zeros and the Riemann Hypothesis
Antonio J. Durán
If and are two formal power series, with , the polynomials defined by the generatin…
Asymptotic for the rightmost zeros of Bell and Eulerian polynomials
Antonio J. Durán
Write , , for the negative zeros of the -th Bell polynomial, ordered in decreasing size. In this paper, we prove the following asymptotic: for a positive…
Misfortunes of a mathematicians' trio using Computer Algebra Systems: Can we trust?
Antonio J. Durán, Mario Pérez, Juan L. Varona
Computer algebra systems are a great help for mathematical research but sometimes unexpected errors in the software can also badly affect it. As an example, we show how we have det…
Using $\D$-operators to construct orthogonal polynomials satisfying higher order difference or differential equations
Antonio J. Durán
We introduce the concept of $\D$-operators associated to a sequence of polynomials and an algebra $\A$ of operators acting in the linear space of polynomials. In this pap…