In this paper, we derive summation formulae for the generalized Legendre-Gould Hopper polynomials (gLeGHP) \({}_SH^{(m)}_n(x,y,z,w)\) and \(\frac{{}_RH^{(m)}_n(x,y,z,w)}{n!}\) by using different analytical means on their respective generating functions. Further, we derive the summation formulae for polynomials related to \({}_SH^{(m)}_n(x,y,z,w)\) and \(\frac{{}_RH^{(m)}_n(x,y,z,w)}{n!}\) as applications of main results. Some concluding remarks are also given.
