000			02755nam a22003858i 4500
001			CR9780511721403
003			UkCbUP
005			20200124160234.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			100303s2008||||enk o ||1 0|eng|d
020			_a9780511721403 (ebook)
020			_z9780521854191 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA404.5 _b.K47 2008
082	0	4	_a515.55 _222
100	1		_aKhrushchev, S. V., _eauthor.
245	1	0	_aOrthogonal polynomials and continued fractions : _bfrom Euler's point of view / _cSergey Khrushchev.
246	3		_aOrthogonal Polynomials & Continued Fractions
264		1	_aCambridge : _bCambridge University Press, _c2008.
300			_a1 online resource (xvi, 478 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aEncyclopedia of mathematics and its applications ; _vvolume 122
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aContinued fractions: real numbers -- Continued fractions: algebra -- Continued fractions: analysis -- Continued fractions: Euler -- Continued fractions: Euler's influence -- P-fractions -- Orthogonal polynomials -- Orthogonal polynomials on the unit circle -- Appendix. Continued fractions, observations L. Euler (1739).
520			_aContinued fractions, studied since Ancient Greece, only became a powerful tool in the eighteenth century, in the hands of the great mathematician Euler. This book tells how Euler introduced the idea of orthogonal polynomials and combined the two subjects, and how Brouncker's formula of 1655 can be derived from Euler's efforts in Special Functions and Orthogonal Polynomials. The most interesting applications of this work are discussed, including the great Markoff's Theorem on the Lagrange spectrum, Abel's Theorem on integration in finite terms, Chebyshev's Theory of Orthogonal Polynomials, and very recent advances in Orthogonal Polynomials on the unit circle. As continued fractions become more important again, in part due to their use in finding algorithms in approximation theory, this timely book revives the approach of Wallis, Brouncker and Euler and illustrates the continuing significance of their influence. A translation of Euler's famous paper 'Continued Fractions, Observation' is included as an Addendum.
600	1	0	_aEuler, Leonhard, _d1707-1783.
650		0	_aOrthogonal polynomials.
650		0	_aContinued fractions.
776	0	8	_iPrint version: _z9780521854191
830		0	_aEncyclopedia of mathematics and its applications ; _vv. 122.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511721403
999			_c517929 _d517927