試證明由給出的第二類切比雪夫多項(xiàng)式族{un(x)}是[-1,1]上個(gè)帶權(quán)的正交多項(xiàng)式.
令T*n(x)=Tn(2x-1),x∈[0,1],試證{T*n(x)}是在[0,1]上帶權(quán)的正交多項(xiàng)式,并求T*0(x),T*1(x),T*2(x),T*3(x).