Journal ArticleDOI
James Stirling’s Methodus Differentialis: An annotated translation of Stirling’s text, by Ian Tweddle. Pp. 295. €129.95, £ 75.00, sFr 210.00, $ 129.00. 2003. ISBN 1 85233 723 0 (Springer).
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In this paper, Euler's use of differentials as absolute zeros, a non-rigorous intuitive approach which was exonerated in retrospect by Abraham Robinson's non-standard model of arithmetic, is discussed.Abstract:
classroom as well as Anthony Ferzola's account of Euler's use of differentials as 'absolute zeros', a non-rigorous intuitive approach which was exonerated in retrospect by Abraham Robinson's non-standard model of arithmetic. It is Euler above all who emerges as a vital and inspirational historical figure whose boldness and imagination can still motivate an intuitive spark in today's students. For these essays alone, this book would be worth its price, but there is much more besides. I can highly recommend it for your library.read more
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FairNAS: Rethinking Evaluation Fairness of Weight Sharing Neural Architecture Search
TL;DR: This paper proves that the biased evaluation of candidate models within a predefined search space is due to inherent unfairness in the supernet training, and proposes two levels of constraints: expectation fairness and strict fairness.
Journal ArticleDOI
Euler's constant: Euler's work and modern developments
TL;DR: A survey of Euler's work on the constant gamma = 0.57721 can be found in this paper, together with some of his related work on gamma function, values of the zeta function and divergent series.
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Close encounters with the Stirling numbers of the second kind
TL;DR: In this article, a historical introduction to the theory of Stirling numbers of the second kind S(n,k) from the point of view of analysis is given. And the reader can also see the connection to Bernoulli numbers, to Euler polynomials and to power sums.
Book ChapterDOI
Asymptotic Approximations to Truncation Errors of Series Representations for Special Functions
TL;DR: Asymptotic approximations to the truncation errors of infinite series for special functions are constructed by solving a system of linear equations as discussed by the authors, which follow from an approximative solution of the inhomogeneous difference equation.
Posted Content
Summation of Divergent Power Series by Means of Factorial Series
TL;DR: In this article, it was shown that factorial series are useful numerical tools for the summation of divergent (inverse) power series, and that the relationship involving Stirling numbers are special cases of more general orthogonal and triangular transformations.
References
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Posted Content
FairNAS: Rethinking Evaluation Fairness of Weight Sharing Neural Architecture Search
TL;DR: This paper proves that the biased evaluation of candidate models within a predefined search space is due to inherent unfairness in the supernet training, and proposes two levels of constraints: expectation fairness and strict fairness.
Journal ArticleDOI
Euler's constant: Euler's work and modern developments
TL;DR: A survey of Euler's work on the constant gamma = 0.57721 can be found in this paper, together with some of his related work on gamma function, values of the zeta function and divergent series.
Journal ArticleDOI
Close Encounters with the Stirling Numbers of the Second Kind
TL;DR: In this paper, a short introduction to the theory of Stirling numbers of the second kind S(m, k) from the point of view of analysis is given, as an historical survey centered on the representation of the Stirling number.
Journal ArticleDOI
Summation of divergent power series by means of factorial series
TL;DR: In this paper, it is shown that factorial series are useful numerical tools for the summation of divergent (inverse) power series, and that the relationship involving Stirling numbers are special cases of more general orthogonal and triangular transformations.
Book ChapterDOI
Asymptotic Approximations to Truncation Errors of Series Representations for Special Functions
TL;DR: Asymptotic approximations to the truncation errors of infinite series for special functions are constructed by solving a system of linear equations as discussed by the authors, which follow from an approximative solution of the inhomogeneous difference equation.