# The generic multiplicity-induced-dominancy property from retarded to neutral delay-differential equations: When delay-systems characteristics meet the zeros of Kummer functions

arXiv: https://arxiv.org/abs/2107.11363 · HTML: https://mlsanity.com/paper/2107.11363/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2021.

## Built on by (most cited first, 1 of 1)

- [A mathematical framework for time-delay reservoir computing analysis](https://mlsanity.com/paper/2603.18706/) (2026)

## Abstract (arXiv)

In this paper, which is a direct continuation and generalization of the recent works by the authors [https://doi.org/10.1051/cocv/2019073, https://doi.org/10.1016/j.jde.2021.03.003], we show the validity of the generic multiplicity-induced-dominancy property for a general class of linear functional differential equations with a single delay, including the retarded as well as the neutral cases. The result is based on an appropriate integral representation of the corresponding characteristic quasipolynomial functions involving some appropriate degenerate hypergeometric functions.