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International Journal of Mathematics and Mathematical Sciences
Volume 14, 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 Hindawi Publishing Corporation. 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 n1, let the nth row of an infinite triangular array consist of entries B(n,j)=nnj(jnj), where 0j[12n].

We develop some properties of this array, which was discovered by Vieta. In addition, we prove some irreducibility properties of the family of polynomials Vn(x)=j=0[12n](1)jB(n,j)xn2j.

These polynomials, which we call Vieta polynomials, are related to Chebychev polynomials of the first kind.