關(guān)于一類非零整系數(shù)互反多項(xiàng)式的Chebyshev變換

王念良，孔 亮

(商洛學(xué)院數(shù)學(xué)與計算科學(xué)系，陜西商洛 726000)

關(guān)于一類非零整系數(shù)互反多項(xiàng)式的Chebyshev變換

王念良，孔 亮

(商洛學(xué)院數(shù)學(xué)與計算科學(xué)系，陜西商洛 726000)

利用第1類、第2類Chebyshev多項(xiàng)式的性質(zhì)，研究了形如P(n，n)(z)=z2n+1，Q(n，n)(z)=z2n+z2n－2+… +z2+1 的非零整系數(shù)互反多項(xiàng)式的 Chebyshev變換，給出了多項(xiàng)式P(mn，mn)(z)，Q(mn－1，mn－1)(z)的 Chebyshev變換公式及一個推論.

第1類Chebyshev多項(xiàng)式;第2類Chebyshev多項(xiàng)式;Chebyshev變換;非零實(shí)系數(shù)互反多項(xiàng)式

1 引言與結(jié)論

2 引理及證明

為了完成定理1的證明，先敘述幾個引理.

3 結(jié)論的證明

推論1的證明 由式(3)和(4)，不難給出推論的證明(略).

［1］王竹溪，郭敦仁.特殊函數(shù)概論［M］.北京:北京大學(xué)出版社，2000:171－172.

［2］KANEMITSU S.On Chebyshev polynomials and some of their application［J］.Journal of Shangluo University，2008，22(5):1 －17.

［3］CANNON J W，WAGREIH Ph.Growth functions of surface Groups［J］.Math.Ann.，1992，293:239 －257.

［4］KWON D.Minimal polynomials of some beta-numbers and Chebyshev polynomials［J］.Acta Arithmetica，2007，130(4):321 －332.

［5］LAKATOS P.On zeros of reciprocal polynomials［J］.Publ.Math.Debracen，2002，61:645 －661.

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

WANG Nian-liang，KONG Liang

(Department of Mathematics and Computing Science，Shangluo University，Shangluo 726000，China)

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 asP(n，n)(z)=z2n+1，Q(n，n)(z)=z2n+z2n－2+ … +z2+1 were studied，and Chebyshev transform formulas on the polynomialsP(mn，mn)(z)，Q(mn－1，mn－1)(z)and a corollary were obtained.

the first kind Chebyshev polynomial;the second kind Chebyshev polynomial;Chebyshev transform;nonzero reciprocal polynomials with real coefficients

O 156.4 < class="emphasis_bold">文獻(xiàn)標(biāo)志碼:A

A

1004－1729(2011)01－0001－03

2010－10－09

陜西省教育廳科研計劃項(xiàng)目支助(2010JK527);商洛學(xué)院科研基金項(xiàng)目(09SKY039)

王念良(1968－)，男，陜西商州人，商洛學(xué)院數(shù)學(xué)與計算科學(xué)系副教授.