Property 2. Leading Coefficient The coefficient of a in TN(a)is 2N-I whenN21
Property 2. Leading Coefficient
Property 3. Symmetry When N= 2M, T2M(a) is an even function, that is 12(-)=T2M(x) 1.77 When N= 2M +1, T2M+1(a)is an odd function, that is, T2M+1(-x)=TM+1(x)
Property 3. Symmetry
Property 4. Trigonometric Representation on[-1,1] TN(x)=cos( N arccos(x)for-1≤x≤1 (1.79)
Property 4. Trigonometric Representation on [-1,1]
Property 5 Distinct Zeros in [-1, 1] TN()has n distinct zeros that lie in the interval [-1, 1(see Figure 4.15) 2k+1)丌 k= coS( 2M ) for k=0, 1,., M These values are called the Chebyshev abscissas(nodes)
Property 5. Distinct Zeros in [-1,1]