Analytic continuation of Lauricella's functions FA(N), FB(N) and FD(N)статья
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Дата последнего поиска статьи во внешних источниках: 9 апреля 2021 г.
Аннотация:We construct formulas for analytic continuation of the Lauricella functions $F_{A}^{(N)}$, $F_{B}^{(N)}$, $F_{D}^{(N)}$ into the exterior of the domains, where they are initially defined by $N$--multiple hypergeometric series. To construct the analytic continuation, we use a new method, which allows to obtain continuation formulas for arbitrary hypergeometric series belonging to Horn's class, which, in particular, contains Lauricella's functions. The obtained formulas give effective apparatus for qualitative analysis and computation of these functions. Thus the results of the paper are of principle significance for numerous applications, where Lauricella's functions appear.