Closed-form evaluation of integrals involving the gamma function

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 integra...

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Published in:Communications in statistics. Theory and methods 2017-09, Vol.46 (17), p.8328-8342
Main Authors: Labib, Richard, de Montigny, Simon
Format: Article
Language:English
Subjects:
Exact solutions
Gamma function
Integrals
Mathematical analysis
mean-time-to-failure
order statistics
Primary 33B20, Secondary 60K10, 62G30
Reliability
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de Montigny, Simon
description 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.
doi_str_mv 10.1080/03610926.2016.1179756
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subjects Exact solutions
Gamma function
Integrals
Mathematical analysis
mean-time-to-failure
order statistics
Primary 33B20, Secondary 60K10, 62G30
Reliability
title Closed-form evaluation of integrals involving the gamma function
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