Comment on the orthogonality of the Macdonald functions of imaginary order

Recently, Yakubovich [Opuscula Math. 26 (2006) 161–172] and Passian et al. [J. Math. Anal. Appl. doi:10.1016/j.jmaa.2009.06.067] have presented alternative proofs of an orthogonality relation obeyed by the Macdonald functions of imaginary order. In this note, we show that the validity of that relation may be also proved in a simpler way by applying a technique occasionally used in mathematical physics to normalize scattering wave functions to the Dirac delta distribution.