# Integral Representation for Borel Sum of Divergent Solution to a Certain Non-Kowalevski Type Equation

### Kunio Ichinobe

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

## Abstract

We shall develop the theory of Borel summability or *k*-summability for a divergent solution of the Cauchy problem for non-Kowalevskian equations of quasihomogeneous type. Precisely, we ﬁrst establish necessary and sufficient conditions for the Borel summability in terms of the Cauchy data (cf. Theorem 2.1), and next we give an integral representation of the Borel sum by using kernel functions which are given by Meijer *G*-function or the generalized hypergeometric functions of conﬂuent type (cf. Theorems 2.3 and 2.6).

## Cite this article

Kunio Ichinobe, Integral Representation for Borel Sum of Divergent Solution to a Certain Non-Kowalevski Type Equation. Publ. Res. Inst. Math. Sci. 39 (2003), no. 4, pp. 657–693

DOI 10.2977/PRIMS/1145476043