20 research outputs found

    A finite class of orthogonal functions generated by Routh-Romanovski polynomials

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    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

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    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

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    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

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    This contribution deals with the sequence {Un(a)(x;q,j)}n≥0\{\mathbb{U}_{n}^{(a)}(x;q,j)\}_{n\geq 0} 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 qq-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 qq-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 Un(a)(x;q,j)\mathbb{U}_{n}^{(a)}(x;q,j), which paves the way to establish an appealing generalization of the so-called JJ-fractions to the framework of Sobolev-type orthogonality.Comment: 2 figure
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