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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.11173 |
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| _version_ | 1866914758198820864 |
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| author | Schmutzhard-Höfler, Sebastian |
| author_facet | Schmutzhard-Höfler, Sebastian |
| contents | We explore integrals of products of Legendre polynomials with a logarithmic weight function. More precisely, for Legendre polynomials $P_m$ and $P_n$ of orders $m$ and $n$, respectively, we provide simple derivations of the integrals $$\int \limits_0^1 P_n(2x-1) P_m(2x-1)\log (x)dx.$$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11173 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A simple derivation of the integrals of products of Legendre polynomials with logarithmic weight Schmutzhard-Höfler, Sebastian Classical Analysis and ODEs We explore integrals of products of Legendre polynomials with a logarithmic weight function. More precisely, for Legendre polynomials $P_m$ and $P_n$ of orders $m$ and $n$, respectively, we provide simple derivations of the integrals $$\int \limits_0^1 P_n(2x-1) P_m(2x-1)\log (x)dx.$$ |
| title | A simple derivation of the integrals of products of Legendre polynomials with logarithmic weight |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2404.11173 |