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