Karp, D. B.López García, José Luis2020-10-282020-10-282017https://academica-e.unavarra.es/handle/2454/38550Esta es la versión no revisada del artículo: D.B. Karp, J.L. López, Representations of hypergeometric functions for arbitrary parameter values and their use, Journal of Approximation Theory, Volume 218, 2017, Pages 42-70, ISSN 0021-9045. Se puede consultar la versión final en https://doi.org/10.1016/j.jat.2017.03.004.Integral representations of hypergeometric functions proved to be a very useful tool for studying their properties. The purpose of this paper is twofold. First, we extend the known representations to arbitrary values of the parameters and show that the extended representations can be interpreted as examples of regularizations of integrals containing Meijer's G function. Second, we give new applications of both, known and extended representations. These include: inverse factorial series expansion for the Gauss type function, new information about zeros of the Bessel and Kummer type functions, connection with radial positive de nite functions and generalizations of Luke's inequalities for the Kummer and Gauss type functions.application/pdfengGeneralized hypergeometric functionMeijer's G functionIntegral representationRadial positive de nite functionInverse factorial seriesHadamard nite partArtículo / ArtikuluaAcceso abierto / Sarbide irekiainfo:eu-repo/semantics/openAccess