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In a recent paper the team of Cogdell, Jorgenson and Smajlovi\'c developinfinite series representations for the logarithmic Mahler measure of a complexlinear form, with 4 or more variables. We establish the case of 3 variables, bybounding an integral with integrand involving the random walk probabilitydensity $a\displaystyle\int_0^\infty tJ_0(at) \displaystyle\prod_{m=0}^2J_0(r_m t)dt$, 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 wedevelop an alternative description of the integral's asymptotic behavior at itsknown points of divergence. As a computational aid to accommodate numericalexperiments, an algorithm to calculate these series is presented in theAppendix.

On an integral of J-Bessel functions and its application to Mahler measure (with an appendix by J.S. Friedman*)