Certain integrals involving logarithmic and exponential functions

In this paper we have evaluated the integrals∫0∞xn−1lnxexp(−ax−bx−1)dxand∫0∞xn−2(ax2−b)(lnx)2exp(−ax−bx−1)dxfor all n=1,2,3,…. Some applications of the results are discussed and an open problem is posed.

Bibliographic Details
Main Authors:	M. Aslam Chaudhry, M. Ahmad
Format:	Article
Language:	English
Published:	Hindawi Limited 1994-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	Macdonald functions logarithmic and exponential function statistical inference theory.
Online Access:	http://dx.doi.org/10.1155/S0161171294000566

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spelling	doaj-243d3c25561c400f9984816080c569ae2020-11-24T21:17:14ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117240540810.1155/S0161171294000566Certain integrals involving logarithmic and exponential functionsM. Aslam Chaudhry0M. Ahmad1Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi ArabiaDepartment of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi ArabiaIn this paper we have evaluated the integrals∫0∞xn−1lnxexp(−ax−bx−1)dxand∫0∞xn−2(ax2−b)(lnx)2exp(−ax−bx−1)dxfor all n=1,2,3,…. Some applications of the results are discussed and an open problem is posed.http://dx.doi.org/10.1155/S0161171294000566Macdonald functionslogarithmic and exponential functionstatistical inference theory.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	M. Aslam Chaudhry M. Ahmad
spellingShingle	M. Aslam Chaudhry M. Ahmad Certain integrals involving logarithmic and exponential functions International Journal of Mathematics and Mathematical Sciences Macdonald functions logarithmic and exponential function statistical inference theory.
author_facet	M. Aslam Chaudhry M. Ahmad
author_sort	M. Aslam Chaudhry
title	Certain integrals involving logarithmic and exponential functions
title_short	Certain integrals involving logarithmic and exponential functions
title_full	Certain integrals involving logarithmic and exponential functions
title_fullStr	Certain integrals involving logarithmic and exponential functions
title_full_unstemmed	Certain integrals involving logarithmic and exponential functions
title_sort	certain integrals involving logarithmic and exponential functions
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1994-01-01
description	In this paper we have evaluated the integrals∫0∞xn−1lnxexp(−ax−bx−1)dxand∫0∞xn−2(ax2−b)(lnx)2exp(−ax−bx−1)dxfor all n=1,2,3,…. Some applications of the results are discussed and an open problem is posed.
topic	Macdonald functions logarithmic and exponential function statistical inference theory.
url	http://dx.doi.org/10.1155/S0161171294000566
work_keys_str_mv	AT maslamchaudhry certainintegralsinvolvinglogarithmicandexponentialfunctions AT mahmad certainintegralsinvolvinglogarithmicandexponentialfunctions
_version_	1726013383967244288

Certain integrals involving logarithmic and exponential functions

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