To avoid inconsistencies, the modern theory of Ramanujan summation requires that "f" is "regular" in the sense that the higher-order derivatives of "f" decay quickly enough for the remainder terms in the Euler–Maclaurin formula to tend to 0. Ramanujan tacitly assumed this property. The regularity requirement prevents the use of Ramanujan summation upon spaced-out series like , because no regular function takes those values. Instead, such a series must be interpreted by zeta function regularization. For this reason, Hardy recommends "great caution" when applying the Ramanujan sums of known series to find the sums of related series.