Several fast algorithms for the approximation of particle-particle interactions by means of multipole expansions in spherical harmonics have appeared recently. In this letter we present a redefinition of the solid spherical harmonics that is real and gives simple expressions for the evaluation of the functions and their derivatives. Application to the recursive bisection method [J. M. Perez-Jorda and W. Yang, Chem. Phys. Lett. 247, 484 (1995)] greatly improves its performance.