Analytic continuation of the Kampé de Fériet function and the general double Horn series

For the Kampé de Fériet function, such analytic continuation formulas are obtained that allow one to represent this function as exponentially converging hypergeometric series in the complement to the convergence domain of the original series. This result has been obtained using the found formulas for the analytic continuation of the Horn series in two variables. © 2022 Informa UK Limited, trading as Taylor & Francis Group.