Supplements to known monotonicity results and inequalities for the gamma and incomplete gamma functions
<p/> <p>We denote by <inline-formula><graphic file="1029-242X-2006-48727-i1.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2006-48727-i2.gif"/></inline-formula> the gamma and the incomplete gamma functions, res...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2006-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2006/48727 |
| Summary: | <p/> <p>We denote by <inline-formula><graphic file="1029-242X-2006-48727-i1.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2006-48727-i2.gif"/></inline-formula> the gamma and the incomplete gamma functions, respectively. In this paper we prove some monotonicity results for the gamma function and extend, to <inline-formula><graphic file="1029-242X-2006-48727-i3.gif"/></inline-formula>, a lower bound established by Elbert and Laforgia (2000) for the function <inline-formula><graphic file="1029-242X-2006-48727-i4.gif"/></inline-formula>, with <inline-formula><graphic file="1029-242X-2006-48727-i5.gif"/></inline-formula>, only for <inline-formula><graphic file="1029-242X-2006-48727-i6.gif"/></inline-formula>.</p> |
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| ISSN: | 1025-5834 1029-242X |