A class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi-Kershaw's inequality

作者：Qi Feng^*

来源：Journal of Computational and Applied Mathematics, 2009, 224(2): 538-543.

DOI：10.1016/j.cam.2008.05.030

• Logarithmically completely monotonic function
• Gautschi-Kershaw's inequality
• Gamma function
• Psi function
• Wallis's ratio

In this article, the logarithmically complete monotonicity of the function
[Gamma(x b)/Gamma(x a)](1/(a-b)) exp vertical bar psi(x c)vertical bar
are discussed, where a. b. c are real numbers and F is the classical Euler's gamma function. From this, the best upper and lower bounds for Walls' ratio Gamma(x 1)/Gamma(x s)
are established, which refine the second Gautschi-Kershaw's inequality.

• 出版日期2009-2-15
• 单位河南理工大学; 河南师范大学