A double inequality related with Burnside’s formula.
Keywords:
Burnside’s formula, Stirling’s formula, Factorial function, InequalitiesAbstract
We prove the following double inequality related with Burnside's formula for n!
where the constants a*=0.428844044... and a*=0.5 are the best possible. We believe that the method we used in the proof gives insight to undergraduate students to understand how simple inequalities can be established.
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References
N. Batir, Inequalities for the gamma function, Archiv Math. (Basel), 91, pp. 554-563, (2008).
W. Burnside, A rapidly convergent series for log N!, Messenger Math., 46, pp. 157-159, (1917).
C-P Chen, On the asymptotic expansions of the gamma function related to the Nemes, Gosper and Burnside formulas, Appl. Math. Comp., 276, pp. 417-431, (2016).
D. Lu, X. Wang, A new asymptotic expansion and some inequalities for the gamma function, J. Number Theory 140, pp. 314-323, (2014).
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