منابع مشابه
Orthogonal basic hypergeometric Laurent polynomials
The Askey-Wilson polynomials are orthogonal polynomials in x = cos θ, which are given as a terminating 4φ3 basic hypergeometric series. The non-symmetric AskeyWilson polynomials are Laurent polynomials in z = eiθ, which are given as a sum of two terminating 4φ3’s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single 4φ3’s which are Laurent polynomials in...
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An ordering for Laurent polynomials in the algebraic torus (C∗)D, inspired by the Cantero–Moral– Velázquez approach to orthogonal Laurent polynomials in the unit circle, leads to the construction of a moment matrix for a given Borel measure in the unit torus T. The Gauss–Borel factorization of this moment matrix allows for the construction of multivariate biorthogonal Laurent polynomials in the...
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We investigate polynomials satisfying a three-term recurrence relation of the form Bn(x) = (x − βn)Bn−1(x) − αnxBn−2(x), with positive recurrence coefficients αn+1, βn (n = 1, 2, . . .). We show that the zeros are eigenvalues of a structured Hessenberg matrix and give the left and right eigenvectors of this matrix, from which we deduce Laurent orthogonality and the Gaussian quadrature formula. ...
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Monotonicity of zeros of orthogonal Laurent polynomials associated with a strong distribution with respect to a parameter is discussed. A natural analog of a classical result of A. Markov is proved. Recent results of Ismail and Muldoon based on the Hellman-Feynman theorem are also extended to a monotonicity criterion for zeros of Laurent polynomials. Results concerning the behaviour of extreme ...
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A three-complex-parameter class of orthogonal Laurent polynomials on the unit circle associated with basic hypergeometric or q-hypergeometric functions is considered. To be precise, we consider the orthogonality properties of the sequence of polynomials { 2Φ1(q−n, qb+1; q−c+b−n; q, qz)}n=0, where 0 < q < 1 and the complex parameters b, c and d are such that b = −1,−2, . . ., c− b+ 1 = −1,−2, . ...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1986
ISSN: 1385-7258
DOI: 10.1016/1385-7258(86)90003-x