Dingle’s rules for deriving the changing forms of an asymptotic expansion as a result
of the Stokes phenomenon are introduced. Of these rules only Nos. 1, 7 and 8 are necessary
for the analysis in later chapters. Then with the aid of these rules his theory of terminants is
presented, which is important because the asymptotic expansions of a multitude of mathematical
functions can be approximated for large values of the summation index by these divergent series
whose coefficients possess gamma function growth. There are basically two types of terminants,
each possessing different properties according to Dingle’s rules. Meaningful values for both types
of terminants are obtained by Borel summation, which is shown to be a method of regularising
asymptotic series.
