000			03747nam a22003858i 4500
001			CR9780511546662
003			UkCbUP
005			20200124160233.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090508s2001||||enk o ||1 0|eng|d
020			_a9780511546662 (ebook)
020			_z9780521790017 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA432 _b.P34 2001
082	0	0	_a515/.723 _221
100	1		_aParis, R. B., _eauthor.
245	1	0	_aAsymptotics and Mellin-Barnes integrals / _cR.B. Paris, D. Kaminski.
246	3		_aAsymptotics & Mellin-Barnes Integrals
264		1	_aCambridge : _bCambridge University Press, _c2001.
300			_a1 online resource (xvi, 422 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 85
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_tOrder Relations -- _tAsymptotic Expansions -- _tOther Expansions -- _tBiographies of Mellin and Barnes -- _tFundamental Results -- _tThe Gamma Function [Gamma] (z) -- _tThe Asymptotic Expansion of [Gamma] (z) -- _tThe Stirling Coefficients -- _tBounds for [Gamma] (z) -- _tExpansion of Quotients of Gamma Functions -- _tInverse Factorial Expansions -- _tA Recursion Formula when [alpha subscript r] = [beta subscript r] -- _tAn Algebraic Method for the Determination of the A[subscript j] -- _tSpecial Cases -- _tThe Asymptotic Expansion of Integral Functions -- _tConvergence of Mellin-Barnes Integrals -- _tOrder Estimates for Remainder Integrals -- _tLemmas -- _tProperties of Mellin Transforms -- _tBasic Properties -- _tTranslational and Differential Properties -- _tThe Parseval Formula -- _tAnalytic Properties -- _tInverse Mellin Transforms -- _tIntegrals Connected with e[superscript -z] -- _tSome Standard Integrals -- _tDiscontinuous Integrals -- _tGamma-Function Integrals -- _tRamanujan-Type Integrals -- _tBarnes' Lemmas -- _tMellin-Barnes Integral Representations -- _tThe Confluent Hypergeometric Functions -- _tThe Gauss Hypergeometric Function -- _tSome Special Functions -- _tApplications of Mellin Transforms -- _tTransformation of Series -- _tThe Mellin Transform Method -- _tThe Poisson-Jacobi Formula -- _tAn Infinite Series -- _tA Smoothed Dirichlet Series -- _tA Finite Sum -- _tNumber-Theoretic Examples -- _tA Harmonic Sum -- _tEuler's Product -- _tRamanujan's Function -- _tSome Other Number-Theoretic Sums -- _tSolution of Differential Equations -- _tPotential Problems in Wedge-Shaped Regions.
520			_aAsymptotics and Mellin-Barnes Integrals, first published in 2001, provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behaviour of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of Mellin-Barnes integrals that is otherwise not available in other standard references on asymptotics.
650		0	_aMellin transform.
650		0	_aAsymptotic expansions.
700	1		_aKaminski, D. _q(David), _d1960- _eauthor.
776	0	8	_iPrint version: _z9780521790017
830		0	_aEncyclopedia of mathematics and its applications ; _vv. 85.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511546662
999			_c517799 _d517797