Property 2. Leading Coefficient The coefficient of in TN()is 2- when N21
Property 2. Leading Coefficient
Property 3. Symmetry When N=2M, T2M(a)is an even function, that is I2M(-x)=12M(x) When N=2M +1, T2M+1( )is an odd function, that is 2M+1(-x)=T2M+1(x) (1.78)
Property 3. Symmetry
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(r) has n distinct zeros that lie in the interval [-1, 1(see Figure 4.15) (2k+1)丌 k=coS ) for k=0, 1,., M 8 2M These values are called the Chebyshev abscissas(nodes)
Property 5. Distinct Zeros in [-1,1]