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003			MX-SnUAN
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007			cr nn 008mamaa
008			150903s2010 gw | o |||| 0|eng d
020			_a9783642050145 _99783642050145
024	7		_a10.1007/9783642050145 _2doi
035			_avtls000354057
039		9	_a201509030534 _bVLOAD _c201405060330 _dVLOAD _y201402181008 _zstaff
040			_aMX-SnUAN _bspa _cMX-SnUAN _erda
050		4	_aQA351
100	1		_aKoekoek, Roelof. _eautor _9338687
245	1	0	_aHypergeometric Orthogonal Polynomials and Their q-Analogues / _cby Roelof Koekoek, Peter A. Lesky, René F. Swarttouw.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2010.
300			_axIx, 578 páginas 2 ilustraciones _brecurso en línea.
336			_atexto _btxt _2rdacontent
337			_acomputadora _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_aarchivo de texto _bPDF _2rda
490	0		_aSpringer Monographs in Mathematics, _x1439-7382
500			_aSpringer eBooks
505	0		_aDefinitions and Miscellaneous Formulas -- Classical orthogonal polynomials -- Orthogonal Polynomial Solutions of Differential Equations -- Orthogonal Polynomial Solutions of Real Difference Equations -- Orthogonal Polynomial Solutions of Complex Difference Equations -- Orthogonal Polynomial Solutions in x(x+u) of Real Difference Equations -- Orthogonal Polynomial Solutions in z(z+u) of Complex Difference Equations -- Hypergeometric Orthogonal Polynomials -- Polynomial Solutions of Eigenvalue Problems -- Classical q-orthogonal polynomials -- Orthogonal Polynomial Solutions of q-Difference Equations -- Orthogonal Polynomial Solutions in q?x of q-Difference Equations -- Orthogonal Polynomial Solutions in q?x+uqx of Real.
520			_aThe very classical orthogonal polynomials named after Hermite, Laguerre and Jacobi, satisfy many common properties. For instance, they satisfy a second-order differential equation with polynomial coefficients and they can be expressed in terms of a hypergeometric function. Replacing the differential equation by a second-order difference equation results in (discrete) orthogonal polynomial solutions with similar properties. Generalizations of these difference equations, in terms of Hahn's q-difference operator, lead to both continuous and discrete orthogonal polynomials with similar properties. For instance, they can be expressed in terms of (basic) hypergeometric functions. Based on Favard's theorem, the authors first classify all families of orthogonal polynomials satisfying a second-order differential or difference equation with polynomial coefficients. Together with the concept of duality this leads to the families of hypergeometric orthogonal polynomials belonging to the Askey scheme. For each family they list the most important properties and they indicate the (limit) relations. Furthermore the authors classify all q-orthogonal polynomials satisfying a second-order q-difference equation based on Hahn's q-operator. Together with the concept of duality this leads to the families of basic hypergeometric orthogonal polynomials which can be arranged in a q-analogue of the Askey scheme. Again, for each family they list the most important properties, the (limit) relations between the various families and the limit relations (for q --> 1) to the classical hypergeometric orthogonal polynomials belonging to the Askey scheme. These (basic) hypergeometric orthogonal polynomials have several applications in various areas of mathematics and (quantum) physics such as approximation theory, asymptotics, birth and death processes, probability and statistics, coding theory and combinatorics.
590			_aPara consulta fuera de la UANL se requiere clave de acceso remoto.
700	1		_aLesky, Peter A. _eautor _9338688
700	1		_aSwarttouw, René F. _eautor _9338689
710	2		_aSpringerLink (Servicio en línea) _9299170
776	0	8	_iEdición impresa: _z9783642050138
856	4	0	_uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-3-642-05014-5 _zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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999			_c301005 _d301005