A Wallis Product on Clovers

Them-clover is the plane curve defined by the polar equation \documentclass{article} \pagestyle{empty}\begin{document} $r^{m/2}=\cos\left(\frac{m}{2}\theta\right)$ \end{document} . In this article we extend a well-known derivation of the Wallis product to derive a generalized Wallis product for arc...

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Bibliographic Details
Published in:The American mathematical monthly 2014-03, Vol.121 (3), p.237-243
Main Author: Hyde, Trevor
Format: Article
Language:English
Subjects:
Arc length
Differential equations
Infinite products
Integers
Mathematical functions
Mathematical problems
Citations: Items that this one cites
Online Access:Get full text
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Summary:Them-clover is the plane curve defined by the polar equation \documentclass{article} \pagestyle{empty}\begin{document} $r^{m/2}=\cos\left(\frac{m}{2}\theta\right)$ \end{document} . In this article we extend a well-known derivation of the Wallis product to derive a generalized Wallis product for arc lengths ofm-clovers.
ISSN:0002-9890
1930-0972
DOI:10.4169/amer.math.monthly.121.03.237