Some Gamma Function Inequalities

Horst Alzer
1993 Mathematics of Computation  
A class of completely monotonie functions are presented involving the gamma function as well as the derivative of the psi function. As a consequence, new upper and lower bounds for the ratio r(x + 1 )/r(x + s) are obtained and compared with related bounds given in part by J. D. Keckic and P. M. Vasic. Our results are further applied to obtain functions which are Laplace transforms of infinitely divisible probability measures.
doi:10.2307/2153171 fatcat:ofnjqmg5fjhglfdegdnilgfu3i