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The Resultant of Chebyshev Polynomials

Published online by Cambridge University Press:  20 November 2018

David P. Jacobs ,
Mohamed O. Rayes  and
Vilmar Trevisan
David P. Jacobs
Affiliation:
School of Computing, Clemson University, Clemson, SC 29634–0974, U.S.A.e-mail: dpj@cs.clemson.edu
Mohamed O. Rayes
Affiliation:
Dept. of Comp. Sci. and Eng., Southern Methodist University, U.S.A.e-mail: mrayes@engr.smu.edu
Vilmar Trevisan
Affiliation:
Instituto de Matemática, UFRGS, Porto Alegre, Brazile-mail: trevisan@mat.ufrgs.br
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Abstract

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Let ${{T}_{n}}$ denote the $n$-th Chebyshev polynomial of the first kind, and let ${{U}_{n}}$ denote the $n$-th Chebyshev polynomial of the second kind. We give an explicit formula for the resultant res$({{T}_{m}},\,{{T}_{n}})$. Similarly, we give a formula for res$({{U}_{m}},\,{{U}_{n}})$.

Keywords

11Y1168W20resultantChebyshev polynomial
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 2 , 01 June 2011 , pp. 288 - 296
Copyright
Copyright © Canadian Mathematical Society 2011

References

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