We propose an algorithm to construct recurrence relations for the coefficients of the Fourier ser... more We propose an algorithm to construct recurrence relations for the coefficients of the Fourier series expansions with respect to the q-classical orthogonal polynomials pk(x;q). Examples dealing with inversion problems, connection between any two sequences of q-classical polynomials, linearization of ϑm(x) pn(x;q), where ϑm(x) is xmor (x;q)m, and the expansion of the Hahn-Exton q-Bessel function in the little q-Jacobi polynomials are
The wave functions of the quantum relativistic harmonic oscillator in configuration space have re... more The wave functions of the quantum relativistic harmonic oscillator in configuration space have recently been shown by Aldaya et al. to be expressed by means of a one-parameter family of polynomials {H^(£)}£ lo-These polynomials are to be called Relativistic Hermite Polynomials (briefly RHP) because they reduce to the well-known classical Hermite polynomials in the non-relativistic limit [N—* co). Here, several algebraic and spectral properties of these polynomials are investigated. As to the former ones, a Rodrigues-type ...
Difference Equations, Special Functions and Orthogonal Polynomials, 2007
ABSTRACT We present a survey on the properties of the Bezout polynomials $A(x)$ and $B(x)$ solvin... more ABSTRACT We present a survey on the properties of the Bezout polynomials $A(x)$ and $B(x)$ solving the Bezout's problem $A(x)P_n(x)+B(x)P_n'(x)=1$, when $P_n(x)$ belongs to an orthogonal polynomial family. We extend results given by P. Humbert for Legendre polynomials on the several recurrences involving the four families $P_n(x), P_n'(x), A(x)$ y $B(x)$ and, from these recurrences, orthogonality of the Bezout pair $(A(x), B(x))$ is stated.
Summary The structural properties of the hypergeometric-type polynomials are, still today, poorl... more Summary The structural properties of the hypergeometric-type polynomials are, still today, poorly known, except those of the classical orthogonal polynomials (i. e. hypergeometric-type polynomials with Favard's orthogonality) in spite of their great usefulness in Mathematical Physics. Here, we study in detail the four-term recurrence and differential-difference relations of the hypergeometric-type polynomials in terms of the coefficients of its second-order differential equation.
1. IntroductionThe Askey scheme of hypergeometric orthogonal polynomials contains the classical o... more 1. IntroductionThe Askey scheme of hypergeometric orthogonal polynomials contains the classical or-thogonal polynomials which can be written in terms of hypergeometric functions, startingat the top with Wilson and Racah polynomials and ending at the bottom with Hermitepolynomials (Askey and Wilson, 1985; Labelle, 1990). Koornwinder (1994) presented aq-Hahn tableau: a q-analogue of that part of the Askey tableau which is dominated byHahn polynomials. In this q-Hahn tableau there are q-analogues of all the families in theAskey tableau, often several q-analogues for one classical family. The q-Hahn tableau isinside a more general scheme of basic hypergeometric orthogonal polynomials (Koekoekand Swarttouw, 1998, see e.g.) dominated by the Askey{Wilson polynomials (Askey andWilson, 1985) and the q-Racah polynomials (Askey and Wilson, 1979), which contain allother families as special or limit cases (Andrews and Askey, 1985).Let fP
considerably extended in the next few years because polynomials orthogonal with respect to a dist... more considerably extended in the next few years because polynomials orthogonal with respect to a distribution function that is equal to a pure polynomial multiplied by a known weight, and among them semiclassical orthogonal polynomials, have a very important role to play in the quantum mechanical treatment of the physical many-body systems. This is so because of the
Abstract When performing model simulations in the field of rotordynamics the classical approach f... more Abstract When performing model simulations in the field of rotordynamics the classical approach for production and subsequent analysis of noisy signals is the addition of white noise to the numerical results. Nevertheless, the noise spectrum observed in monitoring signals from operating rotating machinery rarely resembles white noise; this can be troublesome for noise-reduction filters, usually tuned to deal with white noise. In these machines, signal noise is originated mainly from the interaction of mechanical components with the working fluid flow. Considering this, this manuscript presents a method to simulate the mechanical response of a selected rotor system model to fluid-induced pressure fluctuations, thus increasing modeling accuracy in systems under turbulent-fluid effects. It is supposed that wall pressure fluctuations behave according to the empirical models of Corcos and Goody. A sample of fluid-induced signal noise generated with this method is used to evaluate the robustness of signal processing methods for the detection of single-point rub in aeroderivative gas turbines, while proving how signal features may be affected differently by diverse types of noise. Finally, we present an experimental validation of the methodology on a setup that was adapted to host an axial flow of compressed air throughout the rotor-casing assembly.
We propose an algorithm to construct recurrence relations for the coefficients of the Fourier ser... more We propose an algorithm to construct recurrence relations for the coefficients of the Fourier series expansions with respect to the q-classical orthogonal polynomials pk(x;q). Examples dealing with inversion problems, connection between any two sequences of q-classical polynomials, linearization of ϑm(x) pn(x;q), where ϑm(x) is xmor (x;q)m, and the expansion of the Hahn-Exton q-Bessel function in the little q-Jacobi polynomials are
The wave functions of the quantum relativistic harmonic oscillator in configuration space have re... more The wave functions of the quantum relativistic harmonic oscillator in configuration space have recently been shown by Aldaya et al. to be expressed by means of a one-parameter family of polynomials {H^(£)}£ lo-These polynomials are to be called Relativistic Hermite Polynomials (briefly RHP) because they reduce to the well-known classical Hermite polynomials in the non-relativistic limit [N—* co). Here, several algebraic and spectral properties of these polynomials are investigated. As to the former ones, a Rodrigues-type ...
Difference Equations, Special Functions and Orthogonal Polynomials, 2007
ABSTRACT We present a survey on the properties of the Bezout polynomials $A(x)$ and $B(x)$ solvin... more ABSTRACT We present a survey on the properties of the Bezout polynomials $A(x)$ and $B(x)$ solving the Bezout's problem $A(x)P_n(x)+B(x)P_n'(x)=1$, when $P_n(x)$ belongs to an orthogonal polynomial family. We extend results given by P. Humbert for Legendre polynomials on the several recurrences involving the four families $P_n(x), P_n'(x), A(x)$ y $B(x)$ and, from these recurrences, orthogonality of the Bezout pair $(A(x), B(x))$ is stated.
Summary The structural properties of the hypergeometric-type polynomials are, still today, poorl... more Summary The structural properties of the hypergeometric-type polynomials are, still today, poorly known, except those of the classical orthogonal polynomials (i. e. hypergeometric-type polynomials with Favard's orthogonality) in spite of their great usefulness in Mathematical Physics. Here, we study in detail the four-term recurrence and differential-difference relations of the hypergeometric-type polynomials in terms of the coefficients of its second-order differential equation.
1. IntroductionThe Askey scheme of hypergeometric orthogonal polynomials contains the classical o... more 1. IntroductionThe Askey scheme of hypergeometric orthogonal polynomials contains the classical or-thogonal polynomials which can be written in terms of hypergeometric functions, startingat the top with Wilson and Racah polynomials and ending at the bottom with Hermitepolynomials (Askey and Wilson, 1985; Labelle, 1990). Koornwinder (1994) presented aq-Hahn tableau: a q-analogue of that part of the Askey tableau which is dominated byHahn polynomials. In this q-Hahn tableau there are q-analogues of all the families in theAskey tableau, often several q-analogues for one classical family. The q-Hahn tableau isinside a more general scheme of basic hypergeometric orthogonal polynomials (Koekoekand Swarttouw, 1998, see e.g.) dominated by the Askey{Wilson polynomials (Askey andWilson, 1985) and the q-Racah polynomials (Askey and Wilson, 1979), which contain allother families as special or limit cases (Andrews and Askey, 1985).Let fP
considerably extended in the next few years because polynomials orthogonal with respect to a dist... more considerably extended in the next few years because polynomials orthogonal with respect to a distribution function that is equal to a pure polynomial multiplied by a known weight, and among them semiclassical orthogonal polynomials, have a very important role to play in the quantum mechanical treatment of the physical many-body systems. This is so because of the
Abstract When performing model simulations in the field of rotordynamics the classical approach f... more Abstract When performing model simulations in the field of rotordynamics the classical approach for production and subsequent analysis of noisy signals is the addition of white noise to the numerical results. Nevertheless, the noise spectrum observed in monitoring signals from operating rotating machinery rarely resembles white noise; this can be troublesome for noise-reduction filters, usually tuned to deal with white noise. In these machines, signal noise is originated mainly from the interaction of mechanical components with the working fluid flow. Considering this, this manuscript presents a method to simulate the mechanical response of a selected rotor system model to fluid-induced pressure fluctuations, thus increasing modeling accuracy in systems under turbulent-fluid effects. It is supposed that wall pressure fluctuations behave according to the empirical models of Corcos and Goody. A sample of fluid-induced signal noise generated with this method is used to evaluate the robustness of signal processing methods for the detection of single-point rub in aeroderivative gas turbines, while proving how signal features may be affected differently by diverse types of noise. Finally, we present an experimental validation of the methodology on a setup that was adapted to host an axial flow of compressed air throughout the rotor-casing assembly.
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Papers by A. Zarzo