LEADER 04617nam 22007092 450 001 9910783125203321 005 20151005020622.0 010 $a1-107-12112-4 010 $a1-280-41805-2 010 $a9786610418053 010 $a1-139-14661-0 010 $a0-511-17409-8 010 $a0-511-06706-2 010 $a0-511-06075-0 010 $a0-511-32800-1 010 $a0-511-54666-1 010 $a0-511-06919-7 035 $a(CKB)1000000000017995 035 $a(EBL)217778 035 $a(OCoLC)70756548 035 $a(SSID)ssj0000107024 035 $a(PQKBManifestationID)11138250 035 $a(PQKBTitleCode)TC0000107024 035 $a(PQKBWorkID)10027370 035 $a(PQKB)10534311 035 $a(UkCbUP)CR9780511546662 035 $a(Au-PeEL)EBL217778 035 $a(CaPaEBR)ebr10069865 035 $a(CaONFJC)MIL41805 035 $a(MiAaPQ)EBC217778 035 $a(PPN)261353691 035 $a(EXLCZ)991000000000017995 100 $a20090508d2001|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAsymptotics and Mellin-Barnes integrals /$fR.B. Paris, D. Kaminski$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2001. 215 $a1 online resource (xvi, 422 pages) $cdigital, PDF file(s) 225 1 $aEncyclopedia of mathematics and its applications ;$vvolume 85 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-79001-8 320 $aIncludes bibliographical references (p. [409]-418) and index. 327 $tOrder Relations --$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. 330 $aAsymptotics and Mellin-Barnes Integrals, first published in 2001, provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behaviour of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of Mellin-Barnes integrals that is otherwise not available in other standard references on asymptotics. 410 0$aEncyclopedia of mathematics and its applications ;$vv. 85. 517 3 $aAsymptotics & Mellin-Barnes Integrals 606 $aMellin transform 606 $aAsymptotic expansions 615 0$aMellin transform. 615 0$aAsymptotic expansions. 676 $a515/.723 700 $aParis$b R. B.$0441786 702 $aKaminski$b D$g(David),$f1960- 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910783125203321 996 $aAsymptotics and Mellin-Barnes integrals$93807112 997 $aUNINA