An explicit form and its analytic continuation around the origin of the Borel sum of the Barnes generalized hypergeometric series q__F__p-1 of divergent type (q > p) is obtained. As an application we give an integral representation of the Borel sum of the formal solution to the Cauchy problem of a certain partial differential equation of non-Kowalevski type.
Cite this article
Kunio Ichinobe, The Borel Sum of Divergent Barnes Hypergeometric Series and its Application to a Partial Differential Equation. Publ. Res. Inst. Math. Sci. 37 (2001), no. 1, pp. 91–117DOI 10.2977/PRIMS/1145476691