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1. A perturbation technique can be applied to the Bessel differential equation to determine the following asymptotic expansion for Jo(x) as x x0 : 128 8x 1024 ]win(m)) Use the above expression to develop the asymptotic series to calculate the large roots of Jo(x). Develop the series with three terms. Clearly, the zero-order solution is x - (n - 1/4)rc. Hint: Assume a solution of the form a3 x where a) and as are constants to be determined. Use your solution to fill in the blank entries on the following table: Comparison of Exact Solution of Jo(x) - 0 with the Asymptotic Series Il EXACT ZERO ORDER FIRST ORDER SECOND ORDER (n-1/4) x 1 2.404 8256 2 5.520 0781 3 8.653 7279 4 11.791 5344 5 14.930 9177 6 18.071 0640 7 21.211 6366

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