000 03899nam a22005295i 4500
001 978-3-540-36716-1
003 DE-He213
005 20190213151320.0
007 cr nn 008mamaa
008 100301s2006 gw | s |||| 0|eng d
020 _a9783540367161
_9978-3-540-36716-1
024 7 _a10.1007/b128597
_2doi
050 4 _aQA401-425
072 7 _aPBKJ
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKJ
_2thema
082 0 4 _a511.4
_223
245 1 0 _aOrthogonal Polynomials and Special Functions
_h[electronic resource] :
_bComputation and Applications /
_cedited by Francisco Marcellán, Walter Van Assche.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2006.
300 _aXIV, 422 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1883
505 0 _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.
520 _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.
650 0 _aMathematics.
650 0 _aFunctions, special.
650 0 _aNumerical analysis.
650 0 _aFourier analysis.
650 1 4 _aApproximations and Expansions.
_0http://scigraph.springernature.com/things/product-market-codes/M12023
650 2 4 _aSpecial Functions.
_0http://scigraph.springernature.com/things/product-market-codes/M1221X
650 2 4 _aNumerical Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M14050
650 2 4 _aFourier Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12058
700 1 _aMarcellán, Francisco.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aAssche, Walter Van.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540819349
776 0 8 _iPrinted edition:
_z9783540310624
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1883
856 4 0 _uhttps://doi.org/10.1007/b128597
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c10248
_d10248