Gleichmässige asymptotische Darstellungen für Parameterintegrale mit zwei reellen Parametern

Abstract

Several asymptotic approximations, valid uniformly on certain $\alpha$-intervals, are obtained for a class of integrals depending on two real parameters s and $\alpha$, where $s$ tends to $s_0$. Two cases are considered: a) the integrand has a simple maximum interior to the interval of integration, b) the interval of integration contains no stationary point. In both cases the results still hold true if the stationary point coalesces with the lower limit of integration.