In http://iopscience.iop.org/0305-4470/38/8/005 (A differentiation formula for spherical Bessel functions) Boersma and Glasser proved the following interesting formula $$\left(1-\frac{\sqrt{z^2+a^2}}{z}\,\frac{d}{dz}\right)^n\left[z^{n-1/2} K_{n-1/2}(z)\right]=\left (z+\sqrt{z^2+a^2}\;\right)^nz^{-1/2}K_{1/2}(z),$$ where $K_{n-1/2}(z)$ is a modified Bessel function and $a$ is an arbitrary constant.
It is well known that Bessel functions are related to the matrix elements of the Euclidean motion group (see, for example, http://projecteuclid.org/euclid.tmj/1178244352 -- Bessel functions and the Euclidean motion group, by Akio Orihara, and Vilenkin's book cited in it). Does the Boersma and Glasser relation above have a group theoretic interpretation?
