Results 31 to 40 of about 984,401 (366)
Jointly orthogonal polynomials [PDF]
Journal of the London Mathematical Society, 2015 The theory of polynomials orthogonal with respect to one inner product is classical. We discuss the extension of this theory to multiple inner products. Examples include the Lamé and Heine-Stieltjes polynomials.
Felder, Giovanni, Willwacher, Thomas
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Christoffel transformations for matrix orthogonal polynomials in the real line and the non-Abelian 2D Toda lattice hierarchy [PDF]
, 2015 Given a matrix polynomial $W(x)$, matrix bi-orthogonal polynomials with respect to the sesquilinear form $\langle P(x),Q(x)\rangle_W=\int P(x) W(x)\operatorname{d}\mu(x)(Q(x))^{\top}$, $P(x),Q(x)\in\mathbb R^{p\times p}[x]$, where $\mu(x)$ is a matrix of
Carlos 'Alvarez-Fern'andez +4 more
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Integral of Legendre polynomials and its properties [PDF]
Mathematics and Computational SciencesThis paper is concerned with deriving a new system of orthogonal polynomials whose inflection points coincide with their interior roots, primitives of Legendre polynomials.
Abdelhamid Rehouma
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Zernike polynomials and their applications
Journal of Optics, 2022 The Zernike polynomials are a complete set of continuous functions orthogonal over a unit circle. Since first developed by Zernike in 1934, they have been in widespread use in many fields ranging from optics, vision sciences, to image processing. However,
Kuo Niu, Chao Tian
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Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space
International Journal of Mathematics and Mathematical Sciences, 2004 A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions.
Fred Brackx +2 more
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Проблемы анализа, 2020 In this paper, we give the generating functions of binary product between 2-orthogonal Chebyshev polynomials and kFibonacci, k-Pell, k-Jacobsthal numbers and the other orthogonal Chebyshev polynomials.
H. Merzouk, B. Aloui, A. Boussayoud
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Expected number of real zeros for random linear combinations of orthogonal polynomials [PDF]
, 2015 We study the expected number of real zeros for random linear combinations of orthogonal polynomials. It is well known that Kac polynomials, spanned by monomials with i.i.d.
D. Lubinsky, I. Pritsker, Xiaoju Xie
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Symmetric orthogonal polynomials and the associated orthogonal 𝐿-polynomials [PDF]
Proceedings of the American Mathematical Society, 1995 We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained. Finally as an application, we derive information regarding the orthogonal polynomials associated with the weight function ( 1 + k
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Polynomials orthogonal on the semicircle [PDF]
Journal of Approximation Theory, 1986 The authors study the complex polynomials \(\{\pi_ n\}\) which are orthogonal with respect to the complex-valued inner product \((f,g)=\int^{\pi}_{0}f(e^{i\theta})g(e^{i\theta})d\theta.\) For these polynomials, they obtain a three-term recurrence relation, a linear differential equation of second order and discuss the nature of the zeros.
Gradimir V. Milovanović +1 more
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Representations of orthogonal polynomials
Journal of Computational and Applied Mathematics, 1998 Zeilberger's algorithm provides a method to compute recurrence and differential equations from given hypergeometric series representations, and an adaption of Almquist and Zeilberger computes recurrence and differential equations for hyperexponential integrals.
Dieter Schmersau, Wolfram Koepf
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