Journal of the Ramanujan Mathematical Society

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A Probabilistic Approach To a Conjecture of Ramanujan


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

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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.
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  • A Probabilistic Approach To a Conjecture of Ramanujan

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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.