Asymptotic analysis for confluent hypergeometric function in two variables given by double integral (Q6545236)

The manuscript investigates the asymptotic behavior of confluent hypergeometric functions in two variables, where the solutions are expressed as a double integral of Euler type with resonances among the exponents in the integrand. These functions are derived from Appell's hypergeometric function \( F_4 \) through confluence, resulting in irregular singularities at \( x = \infty \) and \( y = \infty \). The asymptotic behavior of the integrable connection around \( (x, y) = (\infty, \infty) \) is analyzed, and explicit expressions for the Stokes multipliers are obtained.\N\NTechniques are introduced to address resonances, including the construction of higher-dimensional twisted chains, which establish linear relations among twisted cycles and facilitate the computation of Stokes multipliers. Through formal reduction, the main asymptotic behavior of \( F_4 \) function is determined. Methods in asymptotic analysis are employed, supported by illustrative examples, to capture the intricate behavior of solutions around singular points. Furthermore, the results extend Majima's asymptotic expansions to higher-dimensional cases, providing tools applicable to resonant integrable systems.\N\NThe manuscript outlines a framework for analyzing resonant double integrals in asymptotics and integrable systems, offering insights into problems involving irregular singularities in multidimensional systems.