The Chebyshev Equation. The Chebyshev7 differential equation is(1 x2)y xy + 2y = 0,where
Chapter 5, Problem 10(choose chapter or problem)
The Chebyshev Equation. The Chebyshev7 differential equation is(1 x2)y xy + 2y = 0,where is a constant.(a) Determine two solutions in powers of x for |x| < 1, and show that they form afundamental set of solutions.(b) Show that if is a nonnegative integer n, then there is a polynomial solution ofdegree n. These polynomials, when properly normalized, are called the Chebyshevpolynomials. They are very useful in problems that require a polynomial approximationto a function defined on 1 x 1.(c) Find a polynomial solution for each of the cases = n = 0, 1, 2, 3.
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