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.
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Hindawi Limited
1994-01-01
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Series: | International Journal of Mathematics and Mathematical Sciences |
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Online Access: | http://dx.doi.org/10.1155/S0161171294000566 |
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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 |