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Asymptotics and Mellin-Barnes integrals. (English) Zbl 0983.41019
Encyclopedia of Mathematics and Its Applications. 85. Cambridge: Cambridge University Press. xvi, 422 p. (2001).
The book contains eight chapters, beginning with a brief introduction into general notations common in asymptotic analysis and illustrated with the asymptotic behaviour of some special functions. The main tools employed in the asymptotics of integrals are found here, including Watson’s lemma and the method of steepest descent and the notation of optimal truncation. Basic results pertaining to Mellin-Barnes integrals and Mellin transforms are detailed in the next three chapters. The theme of asymptotics is treated in the remaining chapters. The monograph closes with sophisticated applications of the ideas developed in the text to three particular problems, the determination of the asymptotics of the generalized Euler-Jacobi series, expansions for the zeta function on the critical line and the Pearcey integral.
Reviewer: F.Perez Acosta

41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
44A20 Integral transforms of special functions