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Field name	Details
Dewey Class	515
Title	Asymptotics for Orthogonal Polynomials ([EBook] /) / by Walter Van Assche.
Author	Assche, Walter Van
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1987.
Physical Details	VI, 206 p. : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1265
ISBN	9783540477112
Summary Note	Recently there has been a great deal of interest in the theory of orthogonal polynomials. The number of books treating the subject, however, is limited. This monograph brings together some results involving the asymptotic behaviour of orthogonal polynomials when the degree tends to infinity, assuming only a basic knowledge of real and complex analysis. An extensive treatment, starting with special knowledge of the orthogonality measure, is given for orthogonal polynomials on a compact set and on an unbounded set. Another possible approach is to start from properties of the coefficients in the three-term recurrence relation for orthogonal polynomials. This is done using the methods of (discrete) scattering theory. A new method, based on limit theorems in probability theory, to obtain asymptotic formulas for some polynomials is also given. Various consequences of all the results are described and applications are given ranging from random matrices and birth-death processes to discrete Schrödinger operators, illustrating the close interaction with different branches of applied mathematics.:
Contents note	Orthogonal polynomials on a compact set -- Asymptotically periodic recurrence coefficients -- Probabilistic proofs of asymptotic formulas -- Orthogonal polynomials on unbounded sets -- Zero distribution and consequences -- Some applications.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/BFb0081880
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Authors: Assche, Walter Van . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 515 .

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Asymptotics for Orthogonal Polynomials

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