Certain integrals involving logarithmic and exponential functions

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
Description
Summary: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.
ISSN:0161-1712
1687-0425

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