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Author Broucke, R. A.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Keyword Poisson series ♦ Newton iterations ♦ Binomial theorem ♦ Root extraction ♦ Series expansion ♦ Chebyshev series ♦ Fourier series ♦ Series inversion
Abstract Some methods are described for the generation of fractional and negative powers of any formal series, such as Poisson series or Chebyshev series. It is shown that, with the use of the three elementary operations of addition, subtraction, and multiplication, all rational (positive and negative) powers of a series can be constructed. There are basically two approaches: the binomial theorem and the iteration methods. Both methods are described here, and the relationship between them is pointed out. Some well-known classical formulas are obtained as particular cases, and it is shown how the convergence properties of these formulas can be improved with very little additional computations. Finally, at the end of the article, some numerical experiments are described with Chebyshev series and with Fourier series.
Description Affiliation: Univ. of California, Los Angeles (Broucke, R. A.)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2005-08-01
Publisher Place New York
Journal Communications of the ACM (CACM)
Volume Number 14
Issue Number 1
Page Count 4
Starting Page 32
Ending Page 35


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Source: ACM Digital Library