A Refinement of Ramanujan's Factorial Approximation
Michael D. Hirschhorn, Mark B. Villarino
TL;DR
This paper provides elementary proofs for new strict bounds on the correction term in Ramanujan's factorial approximation, enhancing the accuracy and understanding of the classical formula.
Contribution
It introduces novel elementary proofs establishing tighter bounds for the correction term in Ramanujan's factorial approximation.
Findings
New strict upper and lower bounds for the correction term
Elementary proof techniques applied to factorial approximation
Improved understanding of Ramanujan's approximation accuracy
Abstract
We give an elementary proof for new strict upper and lower bounds for the correction term in Ramanujan's approximation for the factorial function
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical Inequalities and Applications · Analytic Number Theory Research