Estimation of the Remainder Term of the Hypergeometric Series $$G_D^{(N,j)}$$

In this paper, new formulas are obtained for estimating the remainder term arising from the summation of the hypergeometric series $$G_D^{(N,j)}$$ . Such formulas allow one to effectively estimate the remainder of the summation when calculating the value of the function $$G_D^{(N,j)}$$ in the unit polydisk. The obtained formulas can be used for calculation of the analytic continuation of the Lauricella function.