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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A new summation method
for power series
with rational coefficients


Authors: Silvia Dassié, Marco Vianello and Renato Zanovello
Journal: Math. Comp. 69 (2000), 749-756
MSC (1991): Primary 65B10, 65D20; Secondary 33E20, 41A60
Published electronically: May 21, 1999
MathSciNet review: 1651749
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that an asymptotic summation method, recently proposed by the authors, can be conveniently applied to slowly convergent power series whose coefficients are rational functions of the summation index. Several numerical examples are presented.


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Additional Information

Silvia Dassié
Affiliation: Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, 35131 Padova, Italy

Marco Vianello
Affiliation: Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, 35131 Padova, Italy
Email: marcov@math.unipd.it

Renato Zanovello
Affiliation: Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, 35131 Padova, Italy
Email: zanov@math.unipd.it

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01113-8
PII: S 0025-5718(99)01113-8
Keywords: Slowly convergent power series, rational coefficients, asymptotic expansions, asymptotic summation
Received by editor(s): April 28, 1998
Published electronically: May 21, 1999
Additional Notes: Work supported, in part, by the Italian MURST, and by the GNIM-CNR
Article copyright: © Copyright 2000 American Mathematical Society