|Journal of Integer Sequences, Vol. 10 (2007), Article 07.3.6|
School of Mathematics and Statistics
The University of Western Australia
Let be the set of such sequences and the additive group of all infinite sequences of integers. Then is a subgroup of and . The methods and results are applied to familiar families of polynomials such as Chebyshev polynomials and shifted Legendre polynomials.
The results are achieved by extending Lagrange interpolation polynomials to power series, using a special basis for the group of integral polynomials, called the integral root basis.
Received October 30 2006; revised version received March 22 2007. Published in Journal of Integer Sequences April 2 2007. Minor revisions, April 17 2008.