LEADER 03646nam 2200625 450 001 996466597303316 005 20210218000957.0 010 $a1-280-63506-1 010 $a9786610635061 010 $a3-540-36716-0 024 7 $a10.1007/b128597 035 $a(CKB)1000000000282900 035 $a(SSID)ssj0000216550 035 $a(PQKBManifestationID)11181480 035 $a(PQKBTitleCode)TC0000216550 035 $a(PQKBWorkID)10197615 035 $a(PQKB)11457109 035 $a(DE-He213)978-3-540-36716-1 035 $a(MiAaPQ)EBC4643097 035 $a(MiAaPQ)EBC6351728 035 $a(PPN)12313031X 035 $a(EXLCZ)991000000000282900 100 $a20210218d2006 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 00$aOrthogonal polynomials and special functions $ecomputation and applications /$fF. Marcella?n, W. van Assche 205 $a1st ed. 2006. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer,$d[2006] 210 4$d©2006 215 $a1 online resource (XIV, 422 p.) 225 1 $aLecture notes in mathematics ;$v1883 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-31062-2 320 $aIncludes bibliographical references and index. 327 $aOrthogonal Polynomials, Quadrature, and Approximation: Computational Methods and Software (in Matlab) -- Equilibrium Problems of Potential Theory in the Complex Plane -- Discrete Orthogonal Polynomials and Superlinear Convergence of Krylov Subspace Methods in Numerical Linear Algebra -- Orthogonal Rational Functions on the Unit Circle: from the Scalar to the Matrix Case -- Orthogonal Polynomials and Separation of Variables -- An Algebraic Approach to the Askey Scheme of Orthogonal Polynomials -- Painlevé Equations ? Nonlinear Special Functions. 330 $aSpecial functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions satisfying linear differential equations, but this has now been extended to difference equations, partial differential equations and non-linear differential equations. The present set of lecture notes containes seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions. The topics are: computational methods and software for quadrature and approximation, equilibrium problems in logarithmic potential theory, discrete orthogonal polynomials and convergence of Krylov subspace methods in numerical linear algebra, orthogonal rational functions and matrix orthogonal rational functions, orthogonal polynomials in several variables (Jack polynomials) and separation of variables, a classification of finite families of orthogonal polynomials in Askey?s scheme using Leonard pairs, and non-linear special functions associated with the Painlevé equations. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1883. 606 $aFunctions, Special 606 $aOrthogonal polynomials 615 0$aFunctions, Special. 615 0$aOrthogonal polynomials. 676 $a515/.55 686 $a31.24$2bcl 702 $aAssche$b Walter van$f1958- 702 $aMarcella?n$b Francisco 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466597303316 996 $aOrthogonal polynomials and special functions$9145975 997 $aUNISA