调和级数的n阶部分和的Ramanujan逼近
Ramanujan's Approximation to the nth Partial Sum of the Harmonic Series
摘要：
一个简单的分部积分法和望远镜取消导致严格的推导的前2项的错误在拉马努金的渐近级数的第n部分和的调和级数。然后，库默尔变换给出了三个更多的条款和严格的误差估计。最后是洛奇近似的最佳估计。
英文摘要：
A simple integration by parts and telescopic cancellation leads to a rigorous derivation of the first 2 terms for the error in Ramanujan's asymptotic series for the nth partial sum of the harmonic series. Then Kummer's transformation gives three more terms and a rigorous error estimate. Finally best-possible estimates of Lodge's approximations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
