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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 resultant, Chebyshev polynomial
MSC Classifications: 11Y11, 68W20 show english descriptions Primality
Randomized algorithms
11Y11 - Primality
68W20 - Randomized algorithms
 

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