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

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).