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Vieta's triangular array and a related family of polynomials

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  • Neville Robbins

Abstract

If n ≥ 1 , let the n t h row of an infinite triangular array consist of entries B ( n , j ) = n n − j ( j n − j ) , where 0 ≤ j ≤ [ 1 2 n ] . We develop some properties of this array, which was discovered by Vieta. In addition, we prove some irreducibility properties of the family of polynomials V n ( x ) = ∑ j = 0 [ 1 2 n ] ( − 1 ) j B ( n , j ) x n − 2 j . These polynomials, which we call Vieta polynomials, are related to Chebychev polynomials of the first kind.

Suggested Citation

  • Neville Robbins, 1991. "Vieta's triangular array and a related family of polynomials," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 14, pages 1-6, January.
    • Handle: RePEc:hin:jijmms:128153
    DOI: 10.1155/S0161171291000261
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