Asymptotic expansions of integrals in complex and real regions

Asymptotic expansions are studied for integrals of holomorphic forms over cycles in the Milnor fibration close to a critical level surface of a holomorphic function. Some regular features are found for the set of exponents in such expansions, and computational results are given. Asymptotic expansions are also considered for real integrals connected with analytic functions. A connection is established between expansions of integrals in a complex region and a real region.