Search Results - Orthogonal polynomials and functions in several variables

Modern trends in constructive function theory : Constructive Functions 2014, conference in honor of Ed Saff's 70th birthday, May 26-30, 2014, Vanderbilt University, Nashville, Tennessee by Hardin, Douglas Patten, Lubinsky, Doron Shaul, Simanek, Brian Z., Constructive Functions (Conference and School)

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Extension of the Beta function in several variables and applications for multivariate orthogonal polynomials by Al-harbi, Nawal Helal, Raïssouli, Mustapha

“… ) from two variables to three or more variables. The properties of such extended functions are studied in a systematic manner and some inequalities are also discussed…”
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On Jacobi Polynomials Of Several Variables by Shrivastava, H.S.P.

“…The aim of the present paper is to define the Jacobi polynomial of two variables, three variables and m-variables…”
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The asymptotics of the kernel functions associated to orthogonal polynomials in several variables on the unit ball by Dueñas, Herbert, Gómez Blanco, Wilmer Merardo

“…We consider a family of orthogonal polynomials in several variables with respect to a Sobolev-type inner product, obtained from adding a gradient operator of order j, evaluated…”
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Moments of Random Matrices and Hypergeometric Orthogonal Polynomials by Cunden, Fabio Deelan, Mezzadri, Francesco, O’Connell, Neil, Simm, Nick

“…We establish a new connection between moments of n × n random matrices X n and hypergeometric orthogonal polynomials…”
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Properties of Some of Two-Variable Orthogonal Polynomials by Milovanović, Gradimir V., Öztürk, Güner, Aktaş, Rabia

“…The present paper deals with various recurrence relations, generating functions and series expansion formulas for two families of orthogonal polynomials in two variables, given Laguerre…”
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Optimal approximants and orthogonal polynomials in several variables by Sargent, Meredith, Sola, Alan A.

“… and orthogonal polynomials in weighted spaces. Weakly inner functions, whose optimal approximants are all constant, provide extreme cases where nontrivial orthogonal polynomials cannot be recovered from the optimal approximants…”
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On Finite Classes of Two-Variable Orthogonal Polynomials by Güldoğan, Esra, Aktaş, Rabia, Masjed-Jamei, Mohammad

“…The purpose of this paper is to introduce several finite sets of orthogonal polynomials in two variables, and investigate some general properties of them such as recurrence relations, generating…”
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Some Sequences of Sobolev-Type Zernike Orthogonal Polynomials by Ruiz, Herbert Dueñas, Combita, Gabriel Pulido

“…In this paper, we study and develop some properties of classical orthogonal polynomials on the unit ball, specifically those that are orthogonal with respect…”
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Inner bounds for the extreme zeros of 3F2 hypergeometric polynomials by Jooste, A., Njionou Sadjang, P., Koepf, W.

“… several variables exist in abundance. We modify Zeilberger's algorithm to generate unknown contiguous relations that are necessary to obtain inner bounds for the extreme zeros of orthogonal polynomial sequences with hypergeometric representations…”
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Sobolev Orthogonal Polynomials of Several Variables on Product Domains by Dueñas Ruiz, Herbert, Salazar-Morales, Omar, Piñar, Miguel

“…Sobolev orthogonal polynomials of d variables on the product domain Ω : = [ a 1 , b 1 ] × ⋯ × [ a d , b d ] with respect to the inner product f , g…”
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Combinatorics of orthogonal polynomials on the unit circle: Combinatorics of orthogonal polynomials on the unit circle by Jang, Jihyeug, Song, Minho

“…Orthogonal polynomials on the unit circle (OPUC for short) are a family of polynomials whose orthogonality is given by integration over the unit circle in the complex plane…”
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Connection coefficients for classical orthogonal polynomials of several variables by Iliev, Plamen, Xu, Yuan

“… For classical orthogonal polynomials whose weights are invariant under the action of the symmetric group, connection coefficients between a basis consisting of products of hypergeometric functions…”
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Combinatorics of orthogonal polynomials of type RI by Kim, Jang Soo, Stanton, Dennis

“…A combinatorial theory for type R I orthogonal polynomials is given. The ingredients include weighted generalized Motzkin paths, moments, continued fractions, determinants, and histories…”
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Sobolev orthogonal polynomials of high order in two variables defined on product domains by Dueñas Ruiz, Herbert, Pinzón-Cortés, Natalia, Salazar-Morales, Omar

“…Let f and g real functions of two variables and We consider the polynomials orthogonal with respect to the inner product…”
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Complex versus real orthogonal polynomials of two variables by Xu, Yuan

“…Orthogonal polynomials of two real variables can often be represented in complex variables…”
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Krall-type orthogonal polynomials in several variables by Fernández, Lidia, Pérez, Teresa E., Piñar, Miguel A., Xu, Yuan

“…For a bilinear form obtained by adding a Dirac mass to a positive definite moment functional defined in the linear space of polynomials in several variables, explicit formulas of orthogonal…”
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A generalization of formulas for the discriminants of quasi-orthogonal polynomials with applications to hypergeometric polynomials by Matsumura, Hideki

“…In this article, we extend the classical framework for computing discriminants of special quasi-orthogonal polynomials…”
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RII type three term relations for bivariate polynomials orthogonal with respect to varying weights by Bracciali, Cleonice F, Delgado, Antonia M, Fernández, Lidia, Pérez, Teresa E

“…Given a bivariate weight function defined on the positive quadrant of R2, we study polynomials in two variables orthogonal with respect to varying measures obtained by special modifications of this weight function…”
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Lax-type pairs in the theory of bivariate orthogonal polynomials by Branquinho, Amílcar, Foulquié-Moreno, Ana, Pérez, Teresa E., Piñar, Miguel A.

“…Sequences of bivariate orthogonal polynomials written as vector polynomials of increasing size satisfy a couple of three term relations with matrix coefficients…”
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