Yang Zhen-Hang, Tian Jing-Feng
1College of Science and Technology, North China Electric Power University, Baoding, P.R. China.
Department of Science and Technology, State Grid Zhejiang Electric Power Company Research Institute, Hangzhou, P.R. China.
J Inequal Appl. 2018;2018(1):272. doi: 10.1186/s13660-018-1870-0. Epub 2018 Oct 5.
In this paper, we present four new Windschitl type approximation formulas for the gamma function. By some unique ideas and techniques, we prove that four functions combined with the gamma function and Windschitl type approximation formulas have good properties, such as monotonicity and convexity. These not only yield some new inequalities for the gamma and factorial functions, but also provide a new proof of known inequalities and strengthen known results.
在本文中，我们给出了四个新的伽马函数的温施蒂尔型近似公式。通过一些独特的思路和技巧，我们证明了四个与伽马函数和温施蒂尔型近似公式相结合的函数具有良好的性质，如单调性和凸性。这些不仅产生了一些关于伽马函数和阶乘函数的新不等式，还为已知不等式提供了新的证明并强化了已知结果。
