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# The Resultant of Chebyshev Polynomials

Published:2011-02-10
Printed: Jun 2011
• David P. Jacobs,
School of Computing, Clemson University, Clemson, SC 29634-0974, U.S.A.
• Mohamed O. Rayes,
Dept. of Comp. Sci. and Eng., Southern Methodist University, U.S.A.
• Vilmar Trevisan,
Instituto de Matemática, UFRGS, Porto Alegre, Brazil
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## Abstract

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 $\operatorname{res}( T_{m}, T_{n} )$. Similarly, we give a formula for $\operatorname{res}( U_{m}, U_{n} )$.
 Keywords: resultant, Chebyshev polynomial
 MSC Classifications: 11Y11 - Primality 68W20 - Randomized algorithms

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