1. The Chebyshev differential equation is given by

d'y

dy

(1-x²) <- x

dx² dx

+ n²y = 0,

where n is a constant.

(a) Solve this equation using the method of Frobenius. Determine the index c and

the recurrence relation.

[5]

(b) Under what circumstances, if any, does the series terminate?

[1]

(c) Find explicit expressions for the first 6 Chebyshev polynomials, To(x) to Ts(x). [4]