 Keeping Grandi's series in mind, this relation explains why ζ(0) = −1⁄2; see also 1 + 1 + 1 + 1 + · · ·.The relation also implies a much more important result.Since "η"("z") and (1 − 21−"z") are both analytic on the entire plane and the latter function's only zero is a simple zero at "z" = 1, it follows that ζ("z") is meromorphic with only a simple pole at "z" = 1.