2016年6月10日
Certain identities on derivatives of radial homogeneous and logarithmic functions
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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.
$k$-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.
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- ID情報
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- arXiv ID : arXiv:1606.06155