论文标题
斯特林的近似值和拉马努扬两个近似之间的隐藏链接
Stirling's approximation and a hidden link between two of Ramanujan's approximations
论文作者
论文摘要
Ramanujan的渐近近似与指数函数与指数积分之间存在猜想的关系。证明涉及斯特林数字，二阶欧拉数，这两者的修改以及斯特林对伽马函数的近似。我们的工作提供了有关Stirling近似系数及其与Ramanujan近似系数的联系的新信息。附录中还包含了更分析的第二证明。
A conjectured relation between Ramanujan's asymptotic approximations to the exponential function and the exponential integral is established. The proof involves Stirling numbers, second-order Eulerian numbers, modifications of both of these, and Stirling's approximation to the gamma function. Our work provides new information about the coefficients in Stirling's approximation and their connection to Ramanujan's approximation coefficients. A more analytic second proof of the main result is also included in an appendix.
