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Zeitschrift für Analysis und ihre Anwendungen


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Volume 2, Issue 2, 1983, pp. 159–173
DOI: 10.4171/ZAA/57

Published online: 1983-04-30

Gleichmässige asymptotische Entwicklungen für Parameterintegrale mit zwei reellen Parametern

Hans-Joachim Schell

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.

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Schell Hans-Joachim: Gleichmässige asymptotische Entwicklungen für Parameterintegrale mit zwei reellen Parametern. Z. Anal. Anwend. 2 (1983), 159-173. doi: 10.4171/ZAA/57