Abstract
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 suitable norm of the derivatives, and give the exact values of the multiples.
Citation
Kei Morii. Tokushi Sato. Yoshihiro Sawano. "Certain Identities on Derivatives of Radial Homogeneous and Logarithmic Functions." Commun. Math. Anal. 9 (2) 51 - 66, 2010.
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