20 research outputs found
A finite class of orthogonal functions generated by Routh-Romanovski polynomials
It is known that some orthogonal systems are mapped onto other orthogonal systems by the Fourier transform. In this article we introduce a finite class of orthogonal functions, which is the Fourier transform of Routh-Romanovski orthogonal polynomials, and obtain its orthogonality relation using Parseval identity
On a moment generalization of some classical second-order differential equations generating classical orthogonal polynomials
The aim of the work is to construct new polynomial systems, which are
solutions to certain functional equations which generalize the second-order
differential equations satisfied by the so called classical orthogonal
polynomial families of Jacobi, Laguerre, Hermite and Bessel. These functional
equations can be chosen to be of different type: fractional differential
equations, q-difference equations, etc, which converge to their respective
differential equations of the aforesaid classical orthogonal polynomials. In
addition to this, there exists a confluence of both the families of polynomials
constructed and the functional equations who approach to the classical families
of polynomials and second-order differential equations, respectivel
On the effect of COVID-19 pandemic in the excess of human mortality. The case of Brazil and Spain
Excess of deaths is a technique used in epidemiology to assess the deaths caused by an unexpected event. For the present COVID-19 pandemic, we discuss the performance of some linear and nonlinear time series forecasting techniques widely used for modeling the actual pandemic and provide estimates for this metric from January 2020 to April 2021. We apply the results obtained to evaluate the evolution of the present pandemic in Brazil and Spain, which allows in particular to compare how well (or bad) these countries have managed the pandemic. For Brazil, our calculations refute the claim made by some officials that the present pandemic is "a little flu". Some studies suggest that the virus could be lying dormant across the world before been detected for the first time. In that regard, our results show that there is no evidence of deaths by the virus in 2019This work was supported in the form of funding in part by Ministerio de Ciencia e Innovacio´n of Spain (Grant No. PID2019-108079GB-C22/AEI/10.13039/501100011033)awarded to N
On second order q-difference equations satisfied by Al-Salam-Carlitz I-Sobolev type polynomials of higher order
This contribution deals with the sequence
of monic polynomials, orthogonal
with respect to a Sobolev-type inner product related to the Al-Salam--Carlitz I
orthogonal polynomials, and involving an arbitrary number of -derivatives on
the two boundaries of the corresponding orthogonality interval. We provide
several versions of the corresponding connection formulas, ladder operators,
and several versions of the second order -difference equations satisfied by
polynomials in this sequence. As a novel contribution to the literature, we
provide certain three term recurrence formula with rational coefficients
satisfied by , which paves the way to establish an
appealing generalization of the so-called -fractions to the framework of
Sobolev-type orthogonality.Comment: 2 figure