On Estimates of Factorial Quotients |
| |
| Authors: | J J Macys |
| |
| Institution: | (1) Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania |
| |
| Abstract: | We consider the factorial quotients (2n − 1)!!/(2n)!! in connection with the Wallis formula n
−1(2n)!!2/(2n − 1)!!2 → π. We improve the Wallis inequalities (n + 1/2)−1(2n)!!2/(2n − 1)!!2 < π < n
−1(2n)!!2/(2n − 1)!!2 for π and obtain new estimates of factorial quotients with error order not worse than 1/n
2.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 349–358, July–September, 2005. |
| |
| Keywords: | Wallis formula number π monotone sequence |
| 本文献已被 SpringerLink 等数据库收录！ |
|
