Work

Mehler Formula for Wronskians of Hermite Polynomials

Year: 2026

Type: article

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 [Ann. Physics 363 (2015), 122-135, arXiv:1502.01778] 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.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2026.111

Authors: Alexey Kuznetsov, Minjian Yuan

Institution: York University

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7163142176

FWCI:

Cites: 14

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Related to: 10