Fourth Order Difference Equation for the Associated Classical Discrete Orthogonal Polynomials PDF Download
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Author: Mama Foupouagnigni
Publisher:
ISBN:
Category : Difference equations
Languages : en
Pages : 6
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Book Description
Abstract: "We derive the fourth order difference equation satisfied by the associated of order [tau] of the classical orthogonal polynomials of a discrete variable. The coefficients of this equation are given in terms of the polynomials [sigma] and [tau] which appear in the discrete Pearson equation [delta]([sigma rho]) = [tau rho] defining the weight [rho]([chi]) of the classical discrete orthogonal polynomials."
Author: Mama Foupouagnigni
Publisher:
ISBN:
Category : Difference equations
Languages : en
Pages : 6
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Book Description
Abstract: "We derive the fourth order difference equation satisfied by the associated of order [tau] of the classical orthogonal polynomials of a discrete variable. The coefficients of this equation are given in terms of the polynomials [sigma] and [tau] which appear in the discrete Pearson equation [delta]([sigma rho]) = [tau rho] defining the weight [rho]([chi]) of the classical discrete orthogonal polynomials."
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Author: Mama Foupouagnigni
Publisher:
ISBN:
Category : Difference equations
Languages : en
Pages : 20
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Book Description
Abstract: "Starting from the D[subscript omega]-Riccati Difference equation satisfied by the Stieltjes function of a linear functional, we work out an algorithm which enables us to write the general fourth-order difference equation satisfied by the associated of any integer order of orthogonal polynomials of the [delta]-Laguerre-Hahn class. Moreover, in classical situations (Meixner, Charlier, Krawtchouk and Hahn), we give these difference equations explicitly; and from the Hahn difference equation, by limit processes we recover the difference equations satisfied by the associated of the classical discrete orthogonal polynomials and the differential equations satisfied by the associated of the classical continuous orthogonal polynomials."
Author: Mama Foupouagnigni
Publisher:
ISBN:
Category :
Languages : en
Pages : 7
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Book Description
Author: Mama Foupouagnigni
Publisher:
ISBN:
Category : Difference equations
Languages : en
Pages : 6
Get Book Here
Book Description
Abstract: "We derive the fourth order q-difference equation satisfied by the first associated of the q-classical orthogonal polynomials. The coefficients of this equation are given in terms of the polynomials [sigma] and [tau] which appear in the q-Pearson difference equation D[subscript q]([sigma rho]) = [tau rho] defining the weight [rho] of the q-classical orthogonal polynomials inside the q-Hahn tableau."
Author: Jan Govaerts
Publisher: World Scientific
ISBN: 9789810249359
Category : Science
Languages : en
Pages : 508
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Book Description
The following topics are discussed in this volume: recent developments in operator theory, coherent states and wavelet analysis, geometric and topological methods in theoretical physics and quantum field theory, and applications of these methods of mathematical physics to problems in atomic and molecular physics as well as the world of the elementary particles and their fundamental interactions. Two extensive sets of lecture notes on quantization techniques in general, and quantum gauge theories and strings as an avenue towards quantum geometry, are also included. The volume should be of interest to anyone working in a field using the mathematical methods associated with any of these topics.
Author: Jan Govaerts
Publisher: World Scientific
ISBN: 9814488682
Category : Science
Languages : en
Pages : 503
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Book Description
The following topics are discussed in this volume: recent developments in operator theory, coherent states and wavelet analysis, geometric and topological methods in theoretical physics and quantum field theory, and applications of these methods of mathematical physics to problems in atomic and molecular physics as well as the world of the elementary particles and their fundamental interactions. Two extensive sets of lecture notes on quantization techniques in general, and quantum gauge theories and strings as an avenue towards quantum geometry, are also included. The volume should be of interest to anyone working in a field using the mathematical methods associated with any of these topics.
Author: Alouf Jirari
Publisher: American Mathematical Soc.
ISBN: 082180359X
Category : Mathematics
Languages : en
Pages : 154
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Book Description
This memoir presents machinery for analyzing many discrete physical situations, and should be of interest to physicists, engineers, and mathematicians. We develop a theory for regular and singular Sturm-Liouville boundary value problems for difference equations, generalizing many of the known results for differential equations. We discuss the self-adjointness of these problems as well as their abstract spectral resolution in the appropriate [italic capital]L2 setting, and give necessary and sufficient conditions for a second-order difference operator to be self-adjoint and have orthogonal polynomials as eigenfunctions.
Author: Jan Govaerts
Publisher: World Scientific
ISBN: 981454292X
Category : Science
Languages : en
Pages : 394
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Book Description
The topics discussed include recent developments in operator theory and orthogonal polynomials, coherent states and wavelet analysis, geometric methods in theoretical physics and quantum field theory, and the application of these methods of mathematical physics to problems in atomic and molecular physics as well as the world of the elementary particles and their fundamental interactions. This volume should be of interest to anyone working in a field using the mathematical methods of any of these general topics.
Author: Howard S. Cohl
Publisher: Cambridge University Press
ISBN: 1108821596
Category : Mathematics
Languages : en
Pages : 351
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Book Description
Contains graduate-level introductions by international experts to five areas of research in orthogonal polynomials and special functions.
Author: Gabor SzegÂ
Publisher: American Mathematical Soc.
ISBN: 0821810235
Category : Mathematics
Languages : en
Pages : 448
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Book Description
The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szego, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the years that have passed since the book first appeared, and with many other books on the subject published since then, this classic monograph by Szego remains an indispensable resource both as a textbook and as a reference book. It can be recommended to anyone who wants to be acquainted with this central topic of mathematical analysis.
