Certain identities on derivatives of radial homogeneous and logarithmic functions

Let k be a natural number and s be real. In the 1-dimensional case, the k-th order derivatives of the functions \lvert x\rvert^s and \log \lvert x\rvert are multiples of \lvert x\rvert^{s-k} and \lvert x\rvert^{-k}, respectively. In the present paper, we generalize this fact to higher dimensions by introducing a... Show more