Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-14T11:17:26.417Z Has data issue: false hasContentIssue false

Beyond the Euler summation formula

Published online by Cambridge University Press:  01 August 2016

Barry Lewis*
Affiliation:
21 Muswell Hill Road, London N10 3JB

Extract

The Eulerian numbers are not strangers to readers of the Gazette but they are not normally associated with the subject of this article, despite the similarity of their names. This article seeks to use Eulerian numbers in generalised telescoping sums, a role that is a powerful extension of an established technique – the Euler summation formula.

Type
Articles
Copyright
Copyright © The Mathematical Association 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Abbott, Steve, A difference method for Σmkpm , Math. Gaz. 79 (July 1995) p. 355.Google Scholar
2. Graham, R. L., Knuth, D. E. and Patashnik, O., Concrete Mathematics (2nd edn), Addison-Wesley (1989).Google Scholar
4. Apostol, Tom, Introduction to analytic number theory, Springer-Verlag (1976) p. 54.Google Scholar
5. Forder, H. G., The Euler-Maclaurin formula, Math. Gaz. 36 (October 1949) p. 172.Google Scholar
6. Hall, R. R., The Euler Maclaurin sum formula, Math. Gaz. 48 (February 1964) p. 80.Google Scholar
7. Gauthier, N., Fibonacci sums of the type ΣrmFr , Math. Gaz. 79 (July 1995) p. 364.Google Scholar