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On properties of hypergeometric type-functions
Cardoso, J. L.; Fernandes, C.; Alvarez-Nodarse, R.The functions of hypergeometric type are the solutions y = y_(z) of the differential equation _(z)y′′+_ (z)y′+_y = 0, where _ and _ are polynomials of degrees not higher than 2 and 1, respectively, and _ is a constant. Here we consider a class of functions of hypergeometric type: those that satisfy the condition […] 0, where _ is an arbitrary complex (fixed) number. We also assume that the coefficients of the p...
Pointwise convergent expansions in q-Fourier-Bessel series
Abreu, L. D.; Alvarez-Nodarse, R.; Cardoso, J. L.We define q-analogues of Fourier-Bessel series, by means of complete q- orthogonal systems constructed with the third Jackson q-Bessel function. Sufficient conditions for pointwise convergence of these series are obtained, in terms of a general convergence principle valid for other Fourier series on grids defined over numerable sets. The results are illustrated with specific examples of developments in q-Fourie...
On some tridiagonal k-Toeplitz matrices: Algebraic and analytical aspects. Appl...
Álvarez-Nodarse, R.; Petronilho, J.; Quintero, N. R.In this paper, we use the analytic theory for 2 and 3-Toeplitz matrices to obtain the explicit expressions for the eigenvalues, eigenvectors and the spectral measure associated to the corresponding infinite matrices. As an application we consider two solvable models related with the so-called chain model. Some numerical experiments are also included. ; http://www.sciencedirect.com/science/article/B6TYH-4FSCV...
On the Krall-type discrete polynomials
Álvarez-Nodarse, R.; Petronilho, J.In this paper we present a unified theory for studying the so-called Krall-type discrete orthogonal polynomials. In particular, the three-term recurrence relation, lowering and raising operators as well as the second order linear difference equation that the sequences of monic orthogonal polynomials satisfy are established. Some relevant examples of q-Krall polynomials are considered in detail. ; http://www....
WKB Approximation and Krall-Type Orthogonal Polynomials
Álvarez-Nodarse, R.; Marcellán, F.; Petronilho, J.We give a unified approach to the Krall-type polynomials orthogonal withrespect to a positive measure consisting of an absolutely continuous one‘perturbed’ by the addition of one or more Dirac deltafunctions. Some examples studied by different authors are considered from aunique point of view. Also some properties of the Krall-type polynomials arestudied. The three-term recurrence relation is calculated explici...
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