On a Class of Polynomials with Integer Coefficients
Department of Mathematics and Informatics
University of Banja Luka
Republic of Srpska, Bosnia and Herzegovina
We define a certain class of polynomials denoted by
Pn,m,p(x), and give the
combinatorial meaning of the coefficients. Chebyshev
polynomials are special cases of Pn,m,p(x).
We first show
can be expressed in terms of Pn,0,p(x).
From this we derive that Pn,2,2(x)
can be obtained in terms of
trigonometric functions, from which we obtain some of its
important properties. Some questions about orthogonality are also addressed.
it is shown that Pn,2,2(x)
fulfills the same three-term recurrence
as the Chebyshev polynomials. We also obtain
some other recurrences for
Pn,m,p(x) and its coefficients.
Finally, we derive
a formula for the coefficients of Chebyshev polynomials of the second kind.
Full version: pdf,
(Concerned with sequences
Received April 12 2008;
revised version received October 29 2008; December 7 2008.
Published in Journal of Integer Sequences, December 11 2008.
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