Several Derivatives of Adjoined Distributions

Abstract:

      A representation theorem for （ｘ±ｉ０）^λｌｎ^k（ｘ±ｉ０） is proved and then the derivatives （ｌｎ^kｘ_±）＇，（ｘ^λ_±ｌｎ^kｘ_±）＇，（ｘ^-n_±ｌｎ^k＇ｘ_±）＇，（ｄ／ｄｘ）｛（ｘ±ｉ０）^λｌｎ^k（ｘ±ｉ０）｝ and （ｄ／ｄｘ）｛（ｘ±ｉ０）^-nｌｎ^k（ｘ±ｉ０）｝ are given.