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Canadian Number Theory Association X Meeting (CNTA X)
July 13-18, 2008
University of Waterloo
Waterloo, Ontario, Canada

Organizers
Kevin Hare (Waterloo, Wentang Kuo (Waterloo), Yu-Ru Liu (Waterloo), David McKinnon (Waterloo), Michael Rubinstein (Waterloo), Cam Stewart (Waterloo)

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Rational Landen Transformations and Divisibility
by
Dante Manna
Dalhousie University
Coauthors: Victor Moll (Tulane University)

Starting in the 18th century, complete elliptic integrals have been known to have a certain

kind of invariance property known as a Landen transformation. In the time since, the

relationship between Landen transformations and iterative means has been somewhat

clarified. We have proven a Landen transformation for rational integrals on the real line, and

for the purposes of adapting to a method of numeric computation of an integral, given an

explicit formula. This formula contains a triple sum of hypergeometric type which exhibits

mysterious divisibility properties.

Date received: June 12, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawl-86.