1. A perturbation technique can be applied to the Bessel differential equation to determine the
following asymptotic expansion for Jo(x) as x
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
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
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