Abstract:
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.
