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arXiv · 2606.02405

Mehler formula for Wronskians of Hermite polynomials

Alexey Kuznetsov·Minjian Yuan
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Abstract

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.

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Alexey Kuznetsov, Minjian Yuan. 2026-06-01. Mehler formula for Wronskians of Hermite polynomials. https://arxiv.org/abs/2606.02405

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