Algebraic Independence of an Airy Function, Its Derivative, and Antiderivative
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913741820395520 |
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| author | Bornemann, Folkmar |
| author_facet | Bornemann, Folkmar |
| contents | Using tools from the Siegel-Shidlovskii theory of transcendental numbers, we prove that a nontrivial solution of the Airy equation, its derivative, and an antiderivative are algebraically independent over the field of rational functions. Courtesy of Michael Singer, the result is also derived from general considerations in differential Galois theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebraic Independence of an Airy Function, Its Derivative, and Antiderivative Bornemann, Folkmar Classical Analysis and ODEs Complex Variables 33C10, 34M15, 11J91, 12H05 Using tools from the Siegel-Shidlovskii theory of transcendental numbers, we prove that a nontrivial solution of the Airy equation, its derivative, and an antiderivative are algebraically independent over the field of rational functions. Courtesy of Michael Singer, the result is also derived from general considerations in differential Galois theory. |
| title | Algebraic Independence of an Airy Function, Its Derivative, and Antiderivative |
| topic | Classical Analysis and ODEs Complex Variables 33C10, 34M15, 11J91, 12H05 |
| url | https://arxiv.org/abs/2502.11852 |