On Gegenbauer polynomials and Wronskian determinants of trigonometric functions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912194068742144 |
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| author | Yuan, Minjian |
| author_facet | Yuan, Minjian |
| contents | M. E. Larsen evaluated the Wronskian determinant of functions $\{\sin(mx)\}_{1\le m \le n}$. We generalize this result and compute the Wronskian of $\{\sin(mx)\}_{1\le m \le n-1}\cup \{\sin((k+n)x\} $. We show that this determinant can be expressed in terms of Gegenbauer orthogonal polynomials and we give two proofs of this result: a direct proof using recurrence relations and a less direct (but, possibly, more instructive) proof based on Darboux-Crum transformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11092 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Gegenbauer polynomials and Wronskian determinants of trigonometric functions Yuan, Minjian Classical Analysis and ODEs Numerical Analysis Probability M. E. Larsen evaluated the Wronskian determinant of functions $\{\sin(mx)\}_{1\le m \le n}$. We generalize this result and compute the Wronskian of $\{\sin(mx)\}_{1\le m \le n-1}\cup \{\sin((k+n)x\} $. We show that this determinant can be expressed in terms of Gegenbauer orthogonal polynomials and we give two proofs of this result: a direct proof using recurrence relations and a less direct (but, possibly, more instructive) proof based on Darboux-Crum transformations. |
| title | On Gegenbauer polynomials and Wronskian determinants of trigonometric functions |
| topic | Classical Analysis and ODEs Numerical Analysis Probability |
| url | https://arxiv.org/abs/2501.11092 |