 A second harmonic mean ("H"1 − X) also exists for this distribution

This harmonic mean with "β" < 1 is undefined because its defining expression is not bounded in [ 0, 1 ].Letting "α" = "β" in the above expression

showing that for "α" = "β" the harmonic mean ranges from 0, for "α" = "β" = 1, to 1/2, for "α" = "β" → ∞.The following are the limits with one parameter finite (non zero) and the other approaching these limits