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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2107.06526 |
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| _version_ | 1866911850027810816 |
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| author | Paulusch, Joachim Schlütter, Sebastian |
| author_facet | Paulusch, Joachim Schlütter, Sebastian |
| contents | We derive the Taylor polynomial of a function, which is $m$-times continuously differentiable and positive homogeneous of order $m$. The Taylor polynomial in $a$ for $f(b)$ of order $m$ in general is a polynomial of order $m$ in $b-a$. If the given function is positive homogeneous of order $m$, the Taylor polynomial is a polynomial in $b$ rather than $b-a$, and the order of all terms is $m$. The result can be applied to powers of homogeneous functions of order $1$ as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_06526 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Taylor Expansion of homogeneous functions Paulusch, Joachim Schlütter, Sebastian General Mathematics 41A10 We derive the Taylor polynomial of a function, which is $m$-times continuously differentiable and positive homogeneous of order $m$. The Taylor polynomial in $a$ for $f(b)$ of order $m$ in general is a polynomial of order $m$ in $b-a$. If the given function is positive homogeneous of order $m$, the Taylor polynomial is a polynomial in $b$ rather than $b-a$, and the order of all terms is $m$. The result can be applied to powers of homogeneous functions of order $1$ as well. |
| title | Taylor Expansion of homogeneous functions |
| topic | General Mathematics 41A10 |
| url | https://arxiv.org/abs/2107.06526 |