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Dec10-07, 07:06 PM
P: 1
Integral of Bessel function

Use the recurrence relation:

[tex]J_{n-1}(x) = \frac{2n}{x} J_{n}(x) - J_{n+1}(x)[/tex]

to write the integral as

[tex]\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[/tex]

then use the relation

[tex] x^n J_{n-1}(x) = \frac{d}{dx}[x^n J_{n}(x)][/tex]

on each of the terms and perform the integration...