# The Borel Sum of Divergent Barnes Hypergeometric Series and its Application to a Partial Differential Equation

### Kunio Ichinobe

Aichi University of Education, Kariya City (Aichi), Japan

## Abstract

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. 91–117

DOI 10.2977/PRIMS/1145476691