000 | 03899nam a22005295i 4500 | ||
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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. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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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 |