Asymptotic formulas for g-gonal sequence factorials

Abstract

In this note, we provide basic asymptotic formulas for approximating large g-gonal sequence factorials by using Stirling and Burnside asymptotic approximation formulas for large factorials. More accurate asymptotic approximation formulas for large g-gonal sequence factorials resulting from some recent, more accurate asymptotic formulas for large factorials that have appeared in the literature are presented.

Keywords:

• sequence factorials
• gamma function
• g-gonal numbers
• Stirling’s formula
• Burnside’s formula

Acknowledgements

The author wishes to thank the referees for the helpful comments which greatly improved the presentation of this note.