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101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aDivergent Series, Summability and Resurgence III$b[electronic resource] $eResurgent Methods and the First Painlevé Equation /$fby Eric Delabaere
205   $a1st ed. 2016.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016.
215   $a1 online resource (XXII, 230 p. 35 illus., 14 illus. in color.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2155
311   $a3-319-28999-3 
327   $aAvant-Propos -- Preface to the three volumes -- Preface to this volume -- Some elements about ordinary differential equations -- The first Painlevé equation -- Tritruncated solutions for the first Painlevé equation -- A step beyond Borel-Laplace summability -- Transseries and formal integral for the first Painlevé equation -- Truncated solutions for the first Painlevé equation -- Supplements to resurgence theory -- Resurgent structure for the first Painlevé equation -- Index.
330   $aThe aim of this volume is two-fold. First, to show how the resurgent methods introduced in volume 1 can be applied efficiently in a non-linear setting; to this end further properties of the resurgence theory must be developed. Second, to analyze the fundamental example of the First Painlevé equation. The resurgent analysis of singularities is pushed all the way up to the so-called ?bridge equation?, which concentrates all information about the non-linear Stokes phenomenon at infinity of the First Painlevé equation. The third in a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists who are interested in divergent power series and related problems, such as the Stokes phenomenon. The prerequisites are a working knowledge of complex analysis at the first-year graduate level and of the theory of resurgence, as presented in volume 1. .
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2155
606   $aSequences (Mathematics)
606   $aDifferential equations
606   $aFunctions of complex variables
606   $aSpecial functions
606   $aSequences, Series, Summability$3https://scigraph.springernature.com/ontologies/product-market-codes/M1218X
606   $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147
606   $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074
606   $aSpecial Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M1221X
615  0$aSequences (Mathematics).
615  0$aDifferential equations.
615  0$aFunctions of complex variables.
615  0$aSpecial functions.
615 14$aSequences, Series, Summability.
615 24$aOrdinary Differential Equations.
615 24$aFunctions of a Complex Variable.
615 24$aSpecial Functions.
676   $a515.24
700   $aDelabaere$b Eric$4aut$4http://id.loc.gov/vocabulary/relators/aut$0730101
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996466770303316
996   $aDivergent series, summability and resurgence III$91748966
997   $aUNISA