以下是一個有關Mobius mu 函數的特殊形式加總式:
summation (k from 1 to infinity){log(k)*μ(k)/k^2}
其中log為自然對數(底數為尤拉數e)
以知此式為絕對收斂,|summation (k from 1 to infinity){log(k)*μ(k)/k^2}|<=summation (k from 1 to infinity){log(k)/k^2}
=integral(k from 1 to infinity){log(k)/k^2}dk=1
因此此加總式必然收斂更為快速,若有人看過此式的實際值,煩請不吝賜教,感謝!