关于一类非零整系数互反多项式的Chebyshev变换

A Kind of Chebyshev Transform of Nonzero Reciprocal Polynomials with Integral Coefficients

利用第1类、第2类Chebyshev多项式的性质,研究了形如P(n,n)(z)=z2n+1,Q(n,n)(z)=z2n+z2n-2+…+z2+1的非零整系数互反多项式的Chebyshev变换,给出了多项式P(mn,mn)(z),Q(mn-1,mn-1)(z)的Cheby-shev变换公式及一个推论.

According to the properties of the first kind and the second kind Chebyshev polynomials,Chebyshev transform of some nonzero reciprocal polynomials with integral coefficients such as P（n,n）（z）=z2n＋1,Q（n,n）（z）=z2n＋z2n-2＋…＋z2＋1 were studied,and Chebyshev transform formulas on the polynomials P（mn,mn）（z）,Q（mn-1,mn-1）（z） and a corollary were obtained.