Logarithmic Completely Monotonic Properties Of Gamma Functions And Their Correlative Properties

Systematic research of Gamma functions for the past several hundreds of years show us the unique nature of Gamma function. There existed many inter-esting thesis such as Gamma functions which were used widely. In this study, our research content based on the existed conclusions, several aspects of the Gamma function, Psi function and Gamma quotient function were studied.Our main results on Gamma function and Psi function included in this thesis are just as following:1.Several inequalities were obtained by studying logarithmically complete monotonicity of the function G(x), H(x) and the quality of v(x), also, some approximations expression of n! were given; We also found the relationship between Gamma functions and exponential average been tenable according to studying the nature of the function fα,β(x).2.The inequality of the Gamma quotient functions were obtained through studying the nature of the Gamma quotient function. Inequality Keckic—Vasic was refined according to studying some special properties of function Gamma.3.Several simple inequalities were draw after several properties related to Psi functions were studied; Application of the new methods in our study leads to that some inequalities existed already may be tenable.