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An orthogonality relation for the Whittaker functions of the second kind ofimaginary order, $W_{\kappa,\mathrm{i}\mu}(x)$, with $\mu\in\mathbb{R}$, isinvestigated. The integral $\int_{0}^{\infty}\mathrm{d}x\:x^{-2}W_{\kappa,\mathrm{i}\mu}(x)W_{\kappa,\mathrm{i}\mu'}(x)$ is shown to beproportional to the sum $\delta(\mu-\mu')+\delta(\mu+\mu')$, where$\delta(\mu\pm\mu')$ is the Dirac delta distribution. The proportionalityfactor is found to be$\pi^{2}/[\mu\sinh(2\pi\mu)\Gamma({1/2}-\kappa+\mathrm{i}\mu)\Gamma({1/2}-\kappa-\mathrm{i}\mu)]$. For $\kappa=0$ the derived formulareduces to the orthogonality relation for the Macdonald functions of imaginaryorder, discussed recently in the literature.

An orthogonality relation for the Whittaker functions of the second kind of imaginary order