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Nonarchimedean Fields and Asymptotic Expansions

1st Edition - January 1, 1975

Authors: A. H. Lightstone, Abraham Robinson

Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 5 7 4 4 - 0

North-Holland Mathematical Library, Volume 13: Nonarchimedean Fields and Asymptotic Expansions focuses on the connection between nonarchimedean systems and the orders of infinity… Read more

Nonarchimedean Fields and Asymptotic Expansions

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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.