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Zeitschrift für Analysis und ihre Anwendungen

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Volume 2, Issue 5, 1983, pp. 427–442
DOI: 10.4171/ZAA/78

Published online: 1983-10-31

Gleichmässige asymptotische Entwicklungen für unvollständige Integrale

Hans-Joachim Schell

A type of integral is considered in which the integrand exp $(—g(s, t))$ has an only maximum in $t = y(s), a(s) < y(s) < b(s)$ for all (real) $s$ near $s_0$, the upper limit is $b$ and the lower limit can vary in $[a,-b]$. For integrals of this type an asymptotic expansion is derived holding for $s \to s_0$ and uniformly with respect to all $x \in [a, b]$. The results are applied to the incomplete gamma function and incomplete beta function.

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Schell Hans-Joachim: Gleichmässige asymptotische Entwicklungen für unvollständige Integrale. Z. Anal. Anwend. 2 (1983), 427-442. doi: 10.4171/ZAA/78