JournalsprimsVol. 37 , No. 1DOI 10.2977/prims/1145476691

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

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.