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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Further inequalities for the gamma function


Author: Andrea Laforgia
Journal: Math. Comp. 42 (1984), 597-600
MSC: Primary 33A15
DOI: https://doi.org/10.1090/S0025-5718-1984-0736455-1
MathSciNet review: 736455
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Abstract: For $ \lambda > 0$ and $ k \geqslant 0$ we present a method which permits us to obtain inequalities of the type $ {(k + \alpha )^{\lambda - 1}} < \Gamma (k + \lambda )/\Gamma (k + 1) < {(k + \beta )^{\lambda - 1}}$, with the usual notation for the gamma function, where $ \alpha $ and $ \beta $ are independent of k. Some examples are also given which improve well-known inequalities. Finally, we are also able to show in some cases that the values $ \alpha $ and $ \beta $ in the inequalities that we obtain cannot be improved.


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DOI: https://doi.org/10.1090/S0025-5718-1984-0736455-1
Article copyright: © Copyright 1984 American Mathematical Society