Equivalence between angular spectrum-based and multipole expansion-based formulas of the acoustic radiation force and torque

Two main methods have been proposed to derive the acoustical radiation force and torque applied by an arbitrary acoustic field on a particle: The first one relies plane wave angular spectrum decomposition of incident (see [Sapozhnikov Bailey, J. Acoust. Soc. Am. 133, 661 (2013)] for [Gong Baudoin, 148, 3131 (2020)] torque), while second into sum spherical waves, so-called multipole expansion [Silva, 130, 3541 (2011)] [Baresh et al., 25 force, [Silva EPL 97, 54003 (2012)] Phys. Rev. Applied 11, 064022 (2019)] torque). In this paper, we formally establish equivalence between expressions obtained with these two both torque.