Since variance is defined as — — (r)2, the variance of the radial position about the mean becomes These results (specifically, the mean) are similar to ones found in the reference by Stumpff [5]; however, the results presented here are derived formally using standard probability techniques for evaluating functions of a random variable. Another statistical quantity of interest is the characteristic function for the orbit radial distribution: We continue by first recalling the Jacobi-Anger [6, 7] relation: where Jn(x) is Bessel’s function of order n. Then, using the identity to integrate the expression for G(a>), the integral can be separated into two parts and integrated separately.
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