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