Real Analysis Exchange

Summation of divergent series from the nonstandard piont of view

Vladimir Kanovei and Michael Reeken

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Abstract

The aim of this paper is to demonstrate that several non-rigorous methods of mathematical reasoning in the field of divergent series, mostly related to the Euler and Hutton transforms, may be developed in a correct and consistent way by methods of nonstandard analysis.

Article information

Source
Real Anal. Exchange, Volume 21, Number 2 (1995), 473-497.

Dates
First available in Project Euclid: 14 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1339694079

Mathematical Reviews number (MathSciNet)
MR1407263

Zentralblatt MATH identifier
0879.03024

Subjects
Primary: 03H05: Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05] 40A25: Approximation to limiting values (summation of series, etc.) {For the Euler-Maclaurin summation formula, see 65B15} 40J05: Summability in abstract structures [See also 43A55, 46A35, 46B15] (should also be assigned at least one other classification number in this section)

Keywords
divergent series summability nonstandard analysis

Citation

Kanovei, Vladimir; Reeken, Michael. Summation of divergent series from the nonstandard piont of view. Real Anal. Exchange 21 (1995), no. 2, 473--497. https://projecteuclid.org/euclid.rae/1339694079


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References

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