000			04174nam a22004455i 4500
001			u373714
003			SIRSI
005			20160812084159.0
007			cr nn 008mamaa
008			100318s2010 gw | s |||| 0|eng d
020			_a9783642050145 _9978-3-642-05014-5
040			_cMX-MeUAM
050		4	_aQA351
082	0	4	_a515.5 _223
100	1		_aKoekoek, Roelof. _eauthor.
245	1	0	_aHypergeometric Orthogonal Polynomials and Their q-Analogues _h[recurso electrónico] / _cby Roelof Koekoek, Peter A. Lesky, René F. Swarttouw.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2010.
300			_aXIX, 578 p. 2 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringer Monographs in Mathematics, _x1439-7382
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.
650		0	_aMathematics.
650		0	_aFunctions, special.
650	1	4	_aMathematics.
650	2	4	_aSpecial Functions.
700	1		_aLesky, Peter A. _eauthor.
700	1		_aSwarttouw, René F. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642050138
830		0	_aSpringer Monographs in Mathematics, _x1439-7382
856	4	0	_zLibro electrónico _uhttp://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-3-642-05014-5
596			_a19
942			_cLIBRO_ELEC
999			_c201594 _d201594