Asymptotics and Mellin-Barnes IntegralsCambridge University Press, 24 de set. 2001 - 422 pàgines Asymptotics 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. |
Altres edicions - Mostra-ho tot
Asymptotics and Mellin-Barnes Integrals R. B. Paris,David Kaminski Previsualització no disponible - 2001 |
Frases i termes més freqüents
Abramowitz & Stegun absolutely convergent algebraic expansion analytic continuation asymptotic expansion asymptotic series back face behaviour Bessel function c-ooi c₁ coefficients computation confluent hypergeometric function corresponding defined denotes difference equation differential equation double pole evaluation example exponential decay exponentially small factor finite gamma function generalised given indented integer integrand integration path internal points inverse factorial expansion Lemma loop m₁ Mellin transform Mellin-Barnes integral representation modulus n₁ Newton diagram nonnegative integer obtain Olver optimal truncation P₁ P₂ parameters path of integration plane positive integer rc+ooi Re(a Re(s Re(v Re(z remainder integral remainder term residue result RM(z saddle point sector separate the poles sequences of poles simple poles solution steepest descent Stirling's formula Stokes line strip of analyticity summation t₁ Titchmarsh 1975 valid values yields zero Σπί
Referències a aquest llibre
Analyzable Functions and Applications: International Workshop on Analyzable ... Ovidiu Costin,Martin David Kruskal,Angus Macintyre Previsualització no disponible - 2005 |