In section 2 of this interesting paper explicit formulae are given for the roots of the transcendental equations \[ s+\gamma k_{\nu}(s^{1/2})=0\quad and\quad s+2\alpha (\beta /4s)^{\nu /2} k_{\nu}(\beta^{1/2}s^{1/2})=0 \] where \(k_{\nu}\) is the modified Bessel function of the second kind of non-negative real order \(\nu\) and \(\gamma\), \(\alpha\), \(\beta\) are real positive constants. In section 3 some asymptotic expressions for the roots are obtained directly from the equations themselves. Next, the equivalence between the results of sections 2 and 3 has been considered. Finally some numerical results based on the findings of section 2 have been presented.