Marcellán Español, Francisco JoséSfaxi, Ridha2023-12-132023-12-132023-04-02Marcellán, F., & Sfaxi, R. (2023). The Cauchy exponential of linear functionals on the linear space of polynomials. Mathematics, 11(8), 1895.2227-7390https://hdl.handle.net/10016/39081In this paper, we introduce the notion of the Cauchy exponential of a linear functional on the linear space of polynomials in one variable with real or complex coefficients using a functional equation by using the so-called moment equation. It seems that this notion hides several properties and results. Our purpose is to explore some of these properties and to compute the Cauchy exponential of some special linear functionals. Finally, a new characterization of the positive-definiteness of a linear functional is given.18eng© 2023 by the authors. Licensee MDPI, Basel, Switzerland.This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.Atribución 3.0 EspañaCauchy exponential of linear functionalCauchy power of linear functionalDu-Laguerre-Hahn operatorOrthogonal polynomial sequencePositive-definite linear functionalRegular linear functionalWeakly-regular linear functionalresearch articleMatemáticashttps://doi.org/10.3390/math11081895open access1818Mathematics11AR/0000033519