(a) When a = n is a nonnegative integer Chebyshev's differential equation always

Chapter 5, Problem 30

(choose chapter or problem)

(a) When a = n is a nonnegative integer Chebyshev's differential equation always possesses a polynomial solution of degree n. Use y1(x) found in to find polynomial solutions for n = 0, n = 2, and n = 4. Then use y2(x) in to find polynomial solutions for n = 1,n = 3, andn = 5. (b) A Chebyshev polynomial Tn(x) is defined to be an nth degree polynomial solution of Chebyshev' s equation multiplied by the constant (-l )n12 when n is even and by (-l )< n-l)/2n when n is odd. Use the solutions found in part (a) to obtain the first six Chebyshev polynomials T0(x), T1(x), ... , T5 (x).