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Closed forms for convolutions of Catalan numbers

Published online by Cambridge University Press:  23 January 2015

N. Gauthier
N. Gauthier*
Affiliation:
Department of Physics, The Royal Military College of Canada, 17000 PO Station Forces, Kingston, ON K7B 7K4, Canada, e-mail:gauthier-n@rmc.ca
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Extract

In Catalan numbers with applications [1], Thomas Koshy gives a clear and accessible account of some of the important characteristics of Catalan numbers. The author also discusses the significance of these numbers for mathematicians, scientists, engineers and amateur enthusiasts alike. The general contents of his book are reviewed in [2]. Catalan numbers, which are named after the mathematician Eugene Catalan (1814-1894), have very interesting and sometimes surprising properties.

Catalan numbers occur in combinatorial mathematics, in particular, where they show up as a natural number sequence that arises in counting problems that usually involve recursively-defined objects.

Type
Articles
Information
The Mathematical Gazette , Volume 96 , Issue 535 , March 2012 , pp. 82 - 90
Copyright
Copyright © The Mathematical Association 2012

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References

1. Koshy, T., Catalan numbers with applications, Oxford University Press (2009).Google Scholar
2. Gauthier, N., Thomas Koshy's Catalan numbers with applications, The Fibonacci Quarterly 48 (February 2010) pp. 85–86.Google Scholar
3. Stanley, Richard and Weisstein, Eric W., Catalan Number, from MathWorld-A Wolfram Web Resource. http://mathworld.wolfram.com/CatalanNumber.html Google Scholar
4. Convolution Theorem: http://en.wikipedia.org/wiki/Convolution_theorem Google Scholar
5. Abramowitz, M. and Stegun, I. A., Handbook of mathematical functions, New York: Dover Publications (1965).Google Scholar
6. Mangulis, V., Handbook of series for scientists and engineers, New York: Academic Press (1965).Google Scholar