A regularized sum is a value assigned to a possibly divergent series by a specified summation or analytic continuation procedure. A regularization is called regular if it assigns every ordinarily convergent series its ordinary sum. A displayed value for a divergent series is therefore incomplete unless the regularization method is also named.
Common methods include Abel-regularized sums, Borel-regularized sums, Hadamard-regularized sums, Hölder-regularized sums, and zeta-regularized sums. These methods need not assign a value to the same classes of series, and distinct methods need not agree outside their common domains.
