Summability method

Summary

A summability method is a rule that assigns a value to some sequences, including some that do not converge. Applied to partial sums, it assigns values to some series. Ordinary convergence is the simplest such rule; Cesàro summation, Abel summation and Borel summation are classical ones that extend it. Summability methods give useful values to divergent series in analysis, number theory and physics. They are studied through properties such as being regular, linear and stable.