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Further Inequalities for the Gamma Function

Andrea Laforgia
Mathematics of Computation
Vol. 42, No. 166 (Apr., 1984), pp. 597-600
DOI: 10.2307/2007604
Stable URL: http://www.jstor.org/stable/2007604
Page Count: 4
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.