A class of k-log-convex functions and their applications to some special functions

作者：Qi Feng^*; Guo Senlin; Guo Bai Ni; Chen Shou Xin

来源：Integral Transforms and Special Functions, 2008, 19(3-4): 195-200.

DOI：10.1080/10652460701722627

• monotonicity
• k-log-convex function
• k-log-concave function
• generalization
• application
• inequality
• gamma function
• Riemann's zeta function
• complete elliptic integrals
• identric mean
• exponential mean
• extended mean values
• special function

Let a and b be two real numbers and f be a positive and differentiable function on an interval L The authors establish the i-log-convex or i-log-concave properties for i is an element of N of the function [f (bx)](a)/[f (ax)](b) for ax is an element of I and bx is an element of I when the function u(k-1) [In f (u)]((k)) for k is an element of N is monotonic and apply these properties to deduce some known and new conclusions related to some special functions, such as the gamma function, Riemann's zeta function, complete elliptic integrals, exponential mean, and extended mean values.

• 出版日期2008-4
• 单位河南理工大学; 河南大学