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 2019.

A system of biorthogonal polynomials with respect to a complex valued measure supported on the unit circle is considered and all the terms with bounds are explicitly given for the remainder of an asymptotic formula given by R. Askey for this system. An electrostatic interpretation for the zeros of a class of para-orthogonal polynomials associated with the biorthogonal system is also considered.

Let µ be a finite positive Borel measure on [−1, 1], m a fixed natural number and L (α,β) We study algebraic and analytic properties of the sequence of monic polynomials (Qn)n>m that satisfy the orthogonality relationsA fluid dynamics model for source points location of a flow of an incompressible fluid with preassigned stagnation points is also considered.

Consider the linear second-order differential equation A n (z)y + B n (z)y + C n y = 0, (1.1) where A n (z) = a 2,n z 2 + a 1,n z + a 0,n with a 2,n = 0, a 2 1,n − 4a 2,n a 0,n = 0, ∀n ∈ N or a 2,n = 0, a 1,n = 0, ∀n ∈ N, B n (z) = b 1,n + b 0,n z are polynomials with complex coefficients and C n ∈ C. Under some assumptions over a certain class of lowering and raising operators, we show that for a sequence of polynomials (φ n) ∞ n=0 orthogonal on the unit circle to satisfy the differential equation (1.1), the polynomial φ n must be of a specific form involving and extension of the Gauss and confluent hypergeometric series.

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