Volume 20, Issue 2, May 2013, Pages 191 - 198
On the Zeros of Polynomials Satisfying Certain Linear Second-Order ODEs Featuring Many Free Parameters
Authors
Francesco Calogero
Dipartimento di Fisica, Universitá di Roma “La Sapienza”, Istituto Nazionale di Fisica Nucleare, Sezione di Roma,francesco.calogero@roma1.infn.it,francesco.calogero@uniroma1.it
Received 19 January 2013, Accepted 21 February 2013, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2013.805565How to use a DOI?
- Keywords
- zeros of polynomials; polynomials satisfying linear second-order ODEs; a linear second-order ODE with only polynomial solutions; Diophantine relations
- Abstract
Certain techniques to obtain properties of the zeros of polynomials satisfying second-order ODEs are reviewed. The application of these techniques to the classical polynomials yields formulas which were already known; new are instead the formulas for the zeros of the (recently identified, and rather explicitly known) polynomials satisfying a (recently identified) second-order ODE which features many free parameters and only polynomial solutions. Some of these formulas have a Diophantine connotation. Techniques to manufacture infinite sequences of second-order ODEs featuring only polynomial solutions are also reported.
- Copyright
- © 2013 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Francesco Calogero PY - 2021 DA - 2021/01/06 TI - On the Zeros of Polynomials Satisfying Certain Linear Second-Order ODEs Featuring Many Free Parameters JO - Journal of Nonlinear Mathematical Physics SP - 191 EP - 198 VL - 20 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2013.805565 DO - 10.1080/14029251.2013.805565 ID - Calogero2021 ER -