Mehler formula for Wronskians of Hermite polynomials
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918535275479040 |
|---|---|
| author | Kuznetsov, Alexey Yuan, Minjian |
| author_facet | Kuznetsov, Alexey Yuan, Minjian |
| contents | We prove that the bilinear generating function for Wronskians of Hermite polynomials can be expressed as the classical Mehler kernel multiplied by a polynomial, thereby extending the result of Pupasov-Maksimov for exceptional Hermite polynomials. We establish several properties of the polynomials appearing in this extended version of the Mehler formula and present four conjectures about them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02405 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mehler formula for Wronskians of Hermite polynomials Kuznetsov, Alexey Yuan, Minjian Classical Analysis and ODEs 26C05, 33C45 We prove that the bilinear generating function for Wronskians of Hermite polynomials can be expressed as the classical Mehler kernel multiplied by a polynomial, thereby extending the result of Pupasov-Maksimov for exceptional Hermite polynomials. We establish several properties of the polynomials appearing in this extended version of the Mehler formula and present four conjectures about them. |
| title | Mehler formula for Wronskians of Hermite polynomials |
| topic | Classical Analysis and ODEs 26C05, 33C45 |
| url | https://arxiv.org/abs/2606.02405 |