Sign In

Communications of the ACM

Communications of the ACM

Construction of rational and negative powers of a formal series

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.

The full text of this article is premium content


No entries found

Log in to Read the Full Article

Sign In

Sign in using your ACM Web Account username and password to access premium content if you are an ACM member, Communications subscriber or Digital Library subscriber.

Need Access?

Please select one of the options below for access to premium content and features.

Create a Web Account

If you are already an ACM member, Communications subscriber, or Digital Library subscriber, please set up a web account to access premium content on this site.

Join the ACM

Become a member to take full advantage of ACM's outstanding computing information resources, networking opportunities, and other benefits.

Subscribe to Communications of the ACM Magazine

Get full access to 50+ years of CACM content and receive the print version of the magazine monthly.

Purchase the Article

Non-members can purchase this article or a copy of the magazine in which it appears.
Sign In for Full Access
» Forgot Password? » Create an ACM Web Account