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

Árpád Elbert1 and Andrea Laforgia2

 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

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.