 Smoothing is a conceptual bridge between zeta function regularization, with its reliance on complex analysis, and Ramanujan summation, with its shortcut to the Euler–Maclaurin formula.Instead, the method operates directly on conservative transformations of the series, using methods from real analysis.The idea is to replace the ill-behaved discrete series formula_11 with a smoothed version
where "f" is a cutoff function with appropriate properties.