  The orbital angular momentum operator expansion turns to be a powerful tool
to construct the fully covariant partial wave amplitudes of hadron decay
reactions and hadron photo- and electroproduction processes. In this paper we
consider a useful development of the orbital angular momentum operator
expansion method. We present the differential technique allowing the direct
calculation of convolutions of two orbital angular momentum operators with an
arbitrary number of open Lorentz indices. This differential technique greatly
simplifies calculations when the reaction subject to the partial wave analysis
involves high spin particles in the initial and/or final states. We also
present a useful generalization of the orbital angular momentum operators.
