A new algorithm for summing divergent series Part 1. Basic theory and illustrations
L.R. Shenton,K. O. Bowman +1 more
TLDR
In this article, the polynomials A(n), B(n) are chosen so that S(1n) has coefficients of powers of n (and n−1) equal to those in a given divergent series T (1n).About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 1976-09-01 and is currently open access. It has received 3 citations till now. The article focuses on the topics: Divergent series & Series (mathematics).read more
Citations
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A new algorithm for summing divergent series
L.R. Shenton,K. O. Bowman +1 more
TL;DR: In this article, Borel models are applied to summing series for the moments of the sample standard deviation, Student's t, and the skewness statistic/b 1. Sampling is from an exponential density.
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Asymptotic series and Stieltjes continued fractions for a gamma function ratio
K.O. Bowman,L.R. Shenton +1 more
TL;DR: In this paper, an analysis for the expansion of a gamma function ratio discussed by Stieltjes and others is given, affording lower and upper bounds, but lacking a rigorous proof.
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A new algorithm for summing divergent series Part 2: A two-component Borel summability model
K. O. Bowman,L.R. Shenton +1 more
TL;DR: In this article, a two-component Borel algorithm with quadratic terms in the integrands involved was proposed as a summing technique for descending series in descending series, and the linear equations which arise have been triangulated, so that approximants to the original series are simple to set up and not as subject to roundoff error as other approaches.
References
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Handbook of Mathematical Functions
Book
A Course of Modern Analysis
TL;DR: The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.
Book
Analytic Theory of Continued Fractions
TL;DR: In this article, a convergence theory of positive definite continued fractions is presented. But the convergence theory is not a generalization of the Stieltjes convergence theorem, and the convergence of continued fractions whose partial denominators are equal to unity is not discussed.