Results 71 to 80 of about 57,584 (243)
Mathematics, 2015 The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials.
Tom Bella, Jenna Reis
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Orthogonal polynomials related to the unit circle and differential-difference equations [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 1997 In this paper we obtain the orthogonal polynomial sequences, related to the unit circle, that verify the following differential-difference equation: (z − α)(z − β)φ'_n(z)/n = (z + αn)φ_n(z) + β_nφ_{n−1}(z) .
A. Cachafeiro, C. Suárez
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A characterization of classical orthogonal Laurent polynomials
Indagationes Mathematicae (Proceedings), 1988 The paper characterizes all Laurent polynomials of the form \[ Q_{2n}(x)=x^{-n}+a^{(2n)}_{-n+1}x^{-n+1}+...+a_ n^{(2n)}x^ n,\quad a_ n^{(2n)}\neq 0, \] \[ Q_{2n+1}(x)=x^{n- 1}+a_{-n}^{(2n+1)}x^{-n}+...+a_ n^{(2n+1)}x^ n,\quad a_ n^{(2n+1)}\neq 0, \] which are orthogonal with respect to a moment functional \({\mathcal L}\). Four examples from the author
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Проблемы анализа, 2019 In this paper, we introduce the notion of Oε-classical orthogonal polynomials, where Oε := I + εD (ε 6= 0). It is shown that the scaled Laguerre polynomial sequence {a −nL (α) n (ax)}n>0, where a = −ε −1 , is actually the only Oε-classical ...
B. Aloui, L. Kheriji
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On some asymptotic properties of classical Hermite polynomials modified by a rational factor
Revista Integración, 2018 In this paper we study some asymptotic properties of the sequence of monic polynomials orthogonal with respect to the measure dµ = x 2+a x2+b e −x 2 dx, where a, b > 0 and a 6= b.
Luis Alejandro Molano Molano
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Discriminants of classical quasi-orthogonal polynomials with application to Diophantine equations
Journal of the Mathematical Society of Japan, 2019 We derive explicit formulas for the discriminants of classical quasi-orthogonal polynomials, as a full generalization of the result of Dilcher and Stolarsky (2005).
M. Sawa, Y. Uchida
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Dual equations and classical orthogonal polynomials
Journal of Mathematical Analysis and Applications, 1968 Abstract : Dual integral equations involving Bessel functions and dual series equations involving Jacobi polynomials occur in several branches of applied mathematics and large classes of these equations can now be solved. We show how many dual sequence equations involving Jacobi and Laguerre polynomials can be solved by similar methods. (Author)
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A Probablistic Origin for a New Class of Bivariate Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2008 We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an ...
Michael R. Hoare, Mizan Rahman
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Orthogonal polynomials and Stieltjes functions: the Laguerre-Hahn case [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 1996 In this paper we consider orthogonal polynomials of the so-called Laguerre-Hahn class. This means that the Stieltjes function associated with the corresponding moment sequence satisfies a Riccati differential equation with polynomial coefficients.
E. PRIANES, F. MARCELLÁN
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The relativistic Laguerre polynomials [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 1996 A new relativistic-type polynomial system is defined by means of the Relativistic Hermite Polynomial system, introduced recently by V.Aldaya et al. to express the wave functions of the quantum relativistic harmonic oscillator.
P. NATALINI
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