Gleichmässige asymptotische Entwicklungen für Parameterintegrale mit zwei reellen Parametern

Abstract

In [8] asymptotic approximations for a class of integrals depending on two real parameters $s,\alpha$ were obtained. They are valid if $s$ tends to $s_0$ and hold uniformly in certain $\alpha$ intervals. Now these results are generalized by deriving asymptotic expansions for the same class of integrals. Again, two cases are considered: a) the integrand has a simple maximum interior to the interval of integration, b) this interval contains no inner stationary point. The results are applied to the Anger function and to the incomplete gamma function.