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Closed-form evaluation of integrals involving the gamma function. (English) Zbl 1375.33007

Summary: In this article, we obtain simplified as well as original closed-form expressions for integrals involving the gamma function. These explicit results are found neither in the literature nor using symbolic computation software. Subsequent results follow, giving rise to explicit expressions for integrals involving the error function, with application in order statistics. In particular, these results can be used within the framework of reliability theory.

MSC:

33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)
60K10 Applications of renewal theory (reliability, demand theory, etc.)
62G30 Order statistics; empirical distribution functions
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