Journal of the Ramanujan Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

A Probabilistic Approach To a Conjecture of Ramanujan


Affiliations
1 Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, United States
     

   Subscribe/Renew Journal


The asymptotic behavior of n-n en n! (1/2-Σ nje-n/j!) was conjectured by Ramanujan to be 1/3 + 4/135(n+kn) where kn ∈ [2/21,8/45]. This conjecture has given rise to serval related problems concerning the asymptotic behavior of series. We shall use some standard results in probability theory to try to better understand these problems.

Keywords

Stirling's Formula, Edgeworth Expansions, Asymptotic Expansions, Large Deviations.
User
Subscription Login to verify subscription
Notifications
Font Size

Abstract Views: 219

PDF Views: 0




  • A Probabilistic Approach To a Conjecture of Ramanujan

Abstract Views: 219  |  PDF Views: 0

Authors

Eric S. Key
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, United States

Abstract


The asymptotic behavior of n-n en n! (1/2-Σ nje-n/j!) was conjectured by Ramanujan to be 1/3 + 4/135(n+kn) where kn ∈ [2/21,8/45]. This conjecture has given rise to serval related problems concerning the asymptotic behavior of series. We shall use some standard results in probability theory to try to better understand these problems.

Keywords


Stirling's Formula, Edgeworth Expansions, Asymptotic Expansions, Large Deviations.