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024 7 $a10.1007/BFb0081880
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035   $a(DE-He213)978-3-540-47711-2
035   $a(MiAaPQ)EBC5585623
035   $a(Au-PeEL)EBL5585623
035   $a(OCoLC)1066199218
035   $a(MiAaPQ)EBC6841981
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100   $a20220908d1987      uy             0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aAsymptotics for orthogonal polynomials /$fWalter Van Assche
205   $a1st ed. 1987.
210  1$aBerlin, Germany ;$aNew York, New York :$cSpringer-Verlag,$d[1987]
210  4$d©1987
215   $a1 online resource (VI, 206 p.)
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1265
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-387-18023-0 
311   $a3-540-18023-0 
327   $aOrthogonal 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.
330   $aRecently there has been a great deal of interest in the theory of orthogonal polynomials. The number of books treating the subject, however, is limited. This monograph brings together some results involving the asymptotic behaviour of orthogonal polynomials when the degree tends to infinity, assuming only a basic knowledge of real and complex analysis. An extensive treatment, starting with special knowledge of the orthogonality measure, is given for orthogonal polynomials on a compact set and on an unbounded set. Another possible approach is to start from properties of the coefficients in the three-term recurrence relation for orthogonal polynomials. This is done using the methods of (discrete) scattering theory. A new method, based on limit theorems in probability theory, to obtain asymptotic formulas for some polynomials is also given. Various consequences of all the results are described and applications are given ranging from random matrices and birth-death processes to discrete Schrödinger operators, illustrating the close interaction with different branches of applied mathematics.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1265
606   $aOrthogonal polynomials$xAsymptotic theory
606   $aMathematical analysis$vCongresses
615  0$aOrthogonal polynomials$xAsymptotic theory.
615  0$aMathematical analysis
676   $a515.55
686   $a42C05$2msc
686   $a33A65$2msc
700   $aAssche$b Walter van$f1958-$0149638
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996466489603316
996   $aAsymptotics for orthogonal polynomials$978533
997   $aUNISA