Antilimit Explained

In mathematics, the antilimit is the equivalent of a limit for a divergent series. The concept not necessarily unique or well-defined, but the general idea is to find a formula for a series and then evaluate it outside its radius of convergence.

Common divergent series

Series	Antilimit
	-1/2
	1/2
	-1/12
	1/4
	0.59634736...
	-1
	1/3
	\gamma

See also

• Abel summation
• Cesàro summation
• Lindelöf summation
• Euler summation
• Borel summation
• Mittag-Leffler summation
• Lambert summation
• Euler–Boole summation and Van Wijngaarden transformation can also be used on divergent series

References

• Shanks . Daniel . An Analogy Between Transients and Mathematical Sequences and Some Nonlinear Sequence-to-Sequence Transforms Suggested by It. Part 1. . Naval Ordnance Lab White Oak Md. . 1949.
• Book: Sidi . Avram . Practical Extrapolation Methods . February 2010 . Cambridge University Press . 9780511546815 . 542. 10.1017/CBO9780511546815.