Further inequalities for the gamma function
Author:
Andrea Laforgia
Journal:
Math. Comp. 42 (1984), 597600
MSC:
Primary 33A15
DOI:
https://doi.org/10.1090/S00255718198407364551
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 wellknown 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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Article copyright:
© Copyright 1984
American Mathematical Society