Nonarchimedean Fields and Asymptotic Expansions

ยท
ยท Elsevier
ืกืคืจ ื“ื™ื’ื™ื˜ืœื™
214
ื“ืคื™ื
ื›ืฉื™ืจ
ื”ื‘ื™ืงื•ืจื•ืช ื•ื”ื“ื™ืจื•ื’ื™ื ืœื ืžืื•ืžืชื™ืย ืžื™ื“ืข ื ื•ืกืฃ

ืžื™ื“ืข ืขืœ ื”ืกืคืจ ื”ื“ื™ื’ื™ื˜ืœื™ ื”ื–ื”

North-Holland Mathematical Library, Volume 13: Nonarchimedean Fields and Asymptotic Expansions focuses on the connection between nonarchimedean systems and the orders of infinity and smallness that are related with the asymptotic behavior of a function. The publication first explains nonarchimedean fields and nonstandard analysis. Discussions focus on the method of mathematical logic, ultrapower construction, principles of permanence, internal functions, many-sorted structures, nonarchimedean fields and groups, and fields with evaluation. The text then discusses the Euler-Maclaurin expansions and the formal concept of asymptotic expansions. Topics include a generalized criterion for asymptotic expansions, asymptotic power series, Watson's Lemma, asymptotic sequences, and the Euler-Maclaurin formula. The manuscript examines Popken space, including asymptotically finite functions, convergence, norm, algebraic properties of the norm, and Popken's description of the norm. The text is a dependable reference for mathematicians and researchers interested in nonarchimedean fields and asymptotic expansions.

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