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Author: Mourad Ismail
Publisher: Cambridge University Press
Published: 2005-11-21
Total Pages: 748
ISBN-13: 9780521782012
DOWNLOAD EBOOKThe first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.
Author: Mourad E. H. Ismail
Publisher:
Published: 2005
Total Pages: 728
ISBN-13: 9781139882811
DOWNLOAD EBOOKThe first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.
Author: Francisco Marcellàn
Publisher: Springer Science & Business Media
Published: 2006-06-19
Total Pages: 432
ISBN-13: 3540310622
DOWNLOAD EBOOKSpecial functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions satisfying linear differential equations, but this has now been extended to difference equations, partial differential equations and non-linear differential equations. The present set of lecture notes containes seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions. The topics are: computational methods and software for quadrature and approximation, equilibrium problems in logarithmic potential theory, discrete orthogonal polynomials and convergence of Krylov subspace methods in numerical linear algebra, orthogonal rational functions and matrix orthogonal rational functions, orthogonal polynomials in several variables (Jack polynomials) and separation of variables, a classification of finite families of orthogonal polynomials in Askey’s scheme using Leonard pairs, and non-linear special functions associated with the Painlevé equations.
Author: Gabor Szeg
Publisher: American Mathematical Soc.
Published: 1939-12-31
Total Pages: 448
ISBN-13: 0821810235
DOWNLOAD EBOOKThe 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.
Author: Howard S. Cohl
Publisher: Cambridge University Press
Published: 2020-10-15
Total Pages: 351
ISBN-13: 1108821596
DOWNLOAD EBOOKContains graduate-level introductions by international experts to five areas of research in orthogonal polynomials and special functions.
Author: Daniel J. Galiffa
Publisher: Springer Science & Business Media
Published: 2013-01-04
Total Pages: 118
ISBN-13: 1461459699
DOWNLOAD EBOOKOn the Higher-Order Sheffer Orthogonal Polynomial Sequences sheds light on the existence/non-existence of B-Type 1 orthogonal polynomials. This book presents a template for analyzing potential orthogonal polynomial sequences including additional higher-order Sheffer classes. This text not only shows that there are no OPS for the special case the B-Type 1 class, but that there are no orthogonal polynomial sequences for the general B-Type 1 class as well. Moreover, it is quite provocative how the seemingly subtle transition from the B-Type 0 class to the B-Type 1 class leads to a drastically more difficult characterization problem. Despite this issue, a procedure is established that yields a definite answer to our current characterization problem, which can also be extended to various other characterization problems as well. Accessible to undergraduate students in the mathematical sciences and related fields, This book functions as an important reference work regarding the Sheffer sequences. The author takes advantage of Mathematica 7 to display unique detailed code and increase the reader's understanding of the implementation of Mathematica 7 and facilitate further experimentation. In addition, this book provides an excellent example of how packages like Mathematica 7 can be used to derive rigorous mathematical results.
Author: M Zuhair Nashed
Publisher: World Scientific
Published: 2018-01-12
Total Pages: 577
ISBN-13: 981322889X
DOWNLOAD EBOOKThis volume aims to highlight trends and important directions of research in orthogonal polynomials, q-series, and related topics in number theory, combinatorics, approximation theory, mathematical physics, and computational and applied harmonic analysis. This collection is based on the invited lectures by well-known contributors from the International Conference on Orthogonal Polynomials and q-Series, that was held at the University of Central Florida in Orlando, on May 10-12, 2015. The conference was dedicated to Professor Mourad Ismail on his 70th birthday.The editors strived for a volume that would inspire young researchers and provide a wealth of information in an engaging format. Theoretical, combinatorial and computational/algorithmic aspects are considered, and each chapter contains many references on its topic, when appropriate.
Author: Jorge Arvesú
Publisher: American Mathematical Soc.
Published: 2010
Total Pages: 314
ISBN-13: 0821848038
DOWNLOAD EBOOKThis volume contains invited lectures and selected contributions from the International Workshop on Orthogonal Polynomials and Approximation Theory, held at Universidad Carlos III de Madrid on September 8-12, 2008, and which honored Guillermo Lopez Lagomasino on his 60th birthday. This book presents the state of the art in the theory of Orthogonal Polynomials and Rational Approximation with a special emphasis on their applications in random matrices, integrable systems, and numerical quadrature. New results and methods are presented in the papers as well as a careful choice of open problems, which can foster interest in research in these mathematical areas. This volume also includes a brief account of the scientific contributions by Guillermo Lopez Lagomasino.
Author: Mohammad Masjed-Jamei
Publisher: Springer Nature
Published: 2020-01-25
Total Pages: 322
ISBN-13: 3030328201
DOWNLOAD EBOOKThis book discusses theoretical and applied aspects of Sturm-Liouville theory and its generalization. It introduces and classifies generalized Sturm-Liouville problems in three different spaces: continuous, discrete, and q-discrete spaces, focusing on special functions that are solutions of a regular or singular Sturm-Liouville problem. Further, it describes the conditions under which the usual Sturm-Liouville problems with symmetric solutions can be extended to a larger class, particularly highlighting the solutions of generalized problems that result in new orthogonal sequences of continuous or discrete functions. Sturm-Liouville theory is central to problems in many areas, such as engineering, mathematics, physics, and biology. This accessibly written book on the topic is a valuable resource for a broad interdisciplinary readership, from novices to experts.
Author: Primitivo B. Acosta Humanez
Publisher: American Mathematical Soc.
Published: 2010
Total Pages: 241
ISBN-13: 0821848860
DOWNLOAD EBOOKPresents the 2007-2008 Jairo Charris Seminar in Algebra and Analysis on Differential Algebra, Complex Analysis and Orthogonal Polynomials, which was held at the Universidad Sergio Arboleda in Bogota, Colombia.
