On the asymptotics for late coefficients in uniform asymptotic expansions of integrals with coalescing saddles
Adri B. Olde Daalhuis · Methods and Applications of Analysis · 2000
We will construct Borel transforms for uniform asymptotic expansions of integrals with coalescing saddles.These Borel transforms are in terms of new functions that have coalescing branch points.The Riemann sheet structures of these clusters of branch points plus a Cauchy type integral representation enable us to obtain asymptotic expansions for the late coefficients of the uniform asymptotic expansions.Two examples involving a Pearcey-type integral are included.