Orthogonal Polynomials
orthogonal polynomials
... This is a mild introduction to the theory of orthogonal polynomials written by a physics prac- titioner. Accordingly, the text does not claim rigor from the point of view of real analysis. Assuming that all ...
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Krall-type orthogonal polynomials in several variables
... of polynomials in several variables, explicit formulas of orthogonal polynomials are derived from the orthogonal polynomials associated with the moment ...
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WKB Approximation and Krall-Type Orthogonal Polynomials
... of polynomials orthogonal with respect to a perturba- tion of a measure via the addition of mass points was introduced by ...new polynomials have been ...of orthogonal polynomials ...
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Moments of random matrices and hypergeometric orthogonal polynomials
... In contrast to the wealth of results on moments as functions of the size n, less attention has been devoted to them as functions of the order k. One of the consequences is that some remarkable properties have been ...
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Orthogonal polynomials from Hermitian matrices. II
... The polynomials discussed in § 3–§ 5 provide new types of exactly solvable birth and death ...(q-Charlier) polynomials are mentioned at the end of § ...classical orthogonal polynomials ...
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A Christoffel–Darboux formula for multiple orthogonal polynomials
... Van Assche et al. [14] found a Riemann–Hilbert problem that characterizes the mul- tiple orthogonal polynomials. This is an extension of the Riemann–Hilbert problem for orthogonal polynomials ...
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Optimal control, Orthogonal Polynomials, Spectral Method, Legendre Polynomials, Riccati Method
... of orthogonal polynomials for obtaining an analytical approximate solution to optimal control problems with a weighed quadratic cost function, is ...the Orthogonal Polynomials for the ...
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Recurrence relations of the multi-indexed orthogonal polynomials
... Ordinary orthogonal polynomials are uniquely characterized by the three term re- currence relations up to an overall multiplicative ...-indexed orthogonal polynomials satisfy 3 + 2 M term ...
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Multivariate Orthogonal Polynomials and Modified Moment Functionals
... of orthogonal polynomials associated with moment functionals fits into a quite general frame that includes families of orthogonal polynomials associated either with positive-definite or non ...
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Asymptotics of derivatives of orthogonal polynomials on the unit circle
... Moreover, by reworking ideas of Nevai, we show that uniform asymptotics for orthogonal polynomials on an arc of the unit circle imply asymptotics for all their derivatives.. © 2006 Elsev[r] ...
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Orthogonal Polynomials of Compact Simple Lie Groups
... and orthogonal polynomials introduced during the last dec- ade are associated with Lie groups or their ...hypergeometric orthogonal polynomials are based on root systems of simple Lie ...
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A New Adaptive Medical Image Coding with Orthogonal Polynomials
... where OPT ( i , j ) is transform coefficient matrix obtained with the orthogonal polynomials transformation. The quantum value matrix Quantum ( i , j ) is obtained through an integer, called quality_factor. ...
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Asymptotics of orthogonal polynomials for a weight with a jump on [-1; 1]
... For the asymptotic analysis we use the steepest descendent method of Deift and Zhou applied to the non-commutative Riemann-Hilbert problems characterizing the orthogonal polynomials. The local analysis at x ...
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On the Christoffel–Darboux formula for generalized matrix orthogonal polynomials
... bi-orthogonal polynomials [5], multiple orthogonal polynomials of mixed type [6] and orthogonal polynomials on the unit circle ...bi-orthogonal polynomials with ...
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8. The $\textbf{D}_{u}$-Classical Orthogonal Polynomials
... give orthogonal polynomials generalizing (by their prop- erties and their characterizations) the classical orthogonal polynomials, but gener- ally it is difficult to explicitly construct them ...
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On \((p,q)\) classical orthogonal polynomials and their characterization theorems
... In the q-case, the solutions of a q-Sturm-Liouville problem are q-orthogonal func- tions [, ], which reduce to the q-classical orthogonal polynomials, appear in a natural way []. Very recently ...
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On the 2 orthogonal polynomials and the generalized birth and death processes
... [5] M. E. H. Ismail, D. R. Masson, J. Letessier, and G. Valent, Birth and death processes and orthog- onal polynomials, Orthogonal Polynomials and Their Applications (Columbus, Ohio, 1989) (P. Nevai, ...
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Towards an Algebraic Theory of Orthogonal Polynomials in Several Variables
... question can be addressed to algebraist is can we obtain such form of recurrence relation if the linear functional is not positive. The answers to these questions open the gate to many future investments towards the ...
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EXPRESSING SUMS OF FINITE PRODUCTS OF CHEBYSHEV POLYNOMIALS OF THE SECOND KIND AND OF FIBONACCI POLYNOMIALS BY SEVERAL ORTHOGONAL POLYNOMIALS
... Abstract. This paper is concerned with representing sums of finite prod- ucts of Chebyshev polynomials of the second kind and of Fibonacci poly- nomials in terms of several classical orthogonal ...
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Representing by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials
... In this section, we will first fix some notations that will be used throughout this paper and then recall the necessary basic facts about orthogonal polynomials. As we will limit the facts to the minimum, the ...
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