  In a recent paper the team of Cogdell, Jorgenson and Smajlovi\'c develop
infinite series representations for the logarithmic Mahler measure of a complex
linear form, with 4 or more variables. We establish the case of 3 variables, by
bounding an integral with integrand involving the random walk probability
density $a\displaystyle\int_0^\infty tJ_0(at) \displaystyle\prod_{m=0}^2
J_0(r_m t)dt$, where $J_0$ is the order zero Bessel function of the first kind,
and $a$ and {$r_m$} are positive real numbers. To facilitate our proof we
develop an alternative description of the integral's asymptotic behavior at its
known points of divergence. As a computational aid to accommodate numerical
experiments, an algorithm to calculate these series is presented in the
Appendix.
