Journal of Inequalities and Applications
Volume 5 (2000), Issue 1, Pages 39-51
doi:10.1155/S1025583400000035
An inequality for the product of two integrals relating to the incomplete gamma function
1Mathematical Institute of the Hungarian Academy of Sciences, R. O. Box 127, Budapest H-1364, Hungary
2Department of Mathematics, Largo S. Leonardo Murialdo, Roma 100146, Italy
Received 26 January 1999; Revised 12 April 1999
Copyright © 2000 Árpád Elbert and Andrea Laforgia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The inequality ∫0xetpdt⋅∫x∞e−tpdt<14 is proved for p>1.87705… and x≥0, and new inequalities are established for the integrals ∫0xetpdt and ∫0xe−tpdt, p>1.