A double inequality related with Burnside’s formula.


  • Necdet Batir Nevşehir Haci Bektas Veli Üniversitesi.


Burnside’s formula, Stirling’s formula, Factorial function, Inequalities


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.

Author Biography

Necdet Batir, Nevşehir Haci Bektas Veli Üniversitesi.

Department of Mathematics.


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).



How to Cite

N. Batir, “A double inequality related with Burnside’s formula.”, Proyecciones (Antofagasta, On line), vol. 37, no. 1, pp. 57-61, Mar. 2018.