Inequalities for the Logarithm of the Gamma Function

Related to Asymptotic Expansions

 

G. Allasia*, C. Giordano* (Speaker), and J. Pecaric**

*Department of Mathematics, University of Turin, Italy

** Faculty of Textile Technology, University of Zagreb, Croatia

 

Many inequalities for the gamma function can be deduced from the convexity properties of some functions related to the logarithm of the gamma function. These inequalities involve finite sums of terms of pertinent asymptotic expansions. Considering a particular case of a generalization of the asymptotic expansion of ln G(x), we give inequalities which overvalue ln G(x), whereas Stirling’s formula undervalue or viceversa. Moreover we obtain inequalities of the same kind for the polygamma function.