Bessel functions are important in such diverse areas as describing planetary motion and
Chapter 9, Problem 45(choose chapter or problem)
Bessel functions are important in such diverse areas as describing planetary motion and the shape of a vibrating drumhead. The Bessel function of order 0 is defined by J(x) = + n=0 (1)nx2n 22n(n!)2 . (a) Find the domain of J(x) by finding the interval of convergence for this power series. (b) Find J(0). (c) Find the partial sum polynomials S0, S1, S2, S3, S4. (d) Estimate J(1) to three decimal places. (e) Use your answer to part (d) to estimate J(1).
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