International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 19381, 10 pages
doi:10.1155/2007/19381
Research Article

Integer Powers of Arcsin

Jonathan M. Borwein1 and Marc Chamberland2

1Faculty of Computer Science, Dalhousie University, Halifax B3H2W5, NS, Canada
2Department of Mathematics and Statistics, Grinnell College, Grinnell 50112, IA, USA

Received 1 November 2006; Revised 28 February 2007; Accepted 18 April 2007

Academic Editor: Ahmed Zayed

Copyright © 2007 Jonathan M. Borwein and Marc Chamberland. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

New simple nested-sum representations for powers of the arcsin function are given. This generalization of Ramanujan's work makes connections to finite binomial sums and polylogarithms.