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    How Do You Integrate x^3 J_0(ax) Over 0 to R?

    Integrals of Bessel Functions Use the recurrence relation: J_{n-1}(x) = \frac{2n}{x} J_{n}(x) - J_{n+1}(x) to write the integral as \int x^3 J_0(x)dx = \int x^3 (\frac{2}{x} J_{1}(x) - J_{2}(x)) dx = \int (2 x^2 J_{1}(x) - x^3 J_{2}(x) ) dx then...
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