Analytic continuation formulas and Jacobi-type relations for Lauricella function

Abstract

An approach for constructing a complete system of formulas for the analytic continuation of the Lauricella generalized hypergeometric function F_D^(N) with any N beyond the boundary of the unit polydisk is proposed. The approach is exposed in detail for the continuation of the function under consideration in neighborhoods of points whose all N components equal 1 or ∞. For the Lauricella function, differential relations being analogues of Jacobi’s formula for the Gaussian hypergeometric function are also presented. The results can be applied to solve the crowding problem for the Schwarz–Christoffel integral and to the theory of the Riemann–Hilbert problem.