International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 2, Pages 239-244
Vieta's triangular array and a related family of polynomials
Department of Mathematics, San Francisco State University, San Francisco 94132, CA, USA
Received 2 November 1988; Revised 12 December 1988
Copyright © 1991 Neville Robbins. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
If , let the row of an infinite triangular array consist of entries
, where .
We develop some properties of this array, which was discovered by Vieta. In addition, we prove
some irreducibility properties of the family of polynomials .
These polynomials, which we call Vieta polynomials, are related to Chebychev polynomials of the