Abstract
For the Lauricella hypergeometric function with an arbitrary number of variables
, we construct formulas for analytic continuation into the vicinity of hyperplanes
and their intersections providing that all variables are close to unit. Such formulas represent the function
near the point
as linear combinations of N–multiple hypergeometric series that are solutions of the same system of partial differential equations as
. Such series are the N–dimensional analog of the Kummer solutions known for the Gauss equation. The constructed analytical continuation formulas allow one to effectively calculate the function
outside the unit polydisk.
Disclosure statement
No potential conflict of interest was reported by the author(s).