Exploring Integration by Differentiation
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910973247356928 |
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| author | George, R. D. Vignat, C. |
| author_facet | George, R. D. Vignat, C. |
| contents | This work validates and extends the method of integration by differentiation, initially introduced by A. Kempf et al., and demonstrates its compatibility with classical rules of integration. It provides applications to classical integrals, including one by Ramanujan, and extends the method to the multivariate setting. Volumes of simplexes are computed by acting with indicator functions on elementary kernels, and a rotationally invariant formulation is derived. Finally, the method is extended to Jackson's q-integral. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22896 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exploring Integration by Differentiation George, R. D. Vignat, C. Classical Analysis and ODEs 26A42, 33F10, 33B15, 44A10, 26B15 This work validates and extends the method of integration by differentiation, initially introduced by A. Kempf et al., and demonstrates its compatibility with classical rules of integration. It provides applications to classical integrals, including one by Ramanujan, and extends the method to the multivariate setting. Volumes of simplexes are computed by acting with indicator functions on elementary kernels, and a rotationally invariant formulation is derived. Finally, the method is extended to Jackson's q-integral. |
| title | Exploring Integration by Differentiation |
| topic | Classical Analysis and ODEs 26A42, 33F10, 33B15, 44A10, 26B15 |
| url | https://arxiv.org/abs/2505.22896 |