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A Gaussian integral formula for the Hermite polynomials: Combinatorics, Asymptotics and Applications
Mihai Nica, Janosch Ortmann
https://arxiv.org/abs/2508.13910 https://…

A Gaussian integral formula for the Hermite polynomials: Combinatorics, Asymptotics and Applications
The Hermite polynomials are ubiquitous but can be difficult to work with due to their unwieldy definition in terms of derivatives. To remedy this, we showcase an underappreciated Gaussian integral formula for the Hermite polynomials, which is especially useful for generalizing to multivariable Hermite polynomials. Taking this as our definition, we prove many useful consequences, including: 1. Combinatorial interpretations for the Hermite polynomials, including a proof of orthogonality. 2. A mor…

Variational data assimilation for the wave equation in heterogeneous media: Numerical investigation of stability
Erik Burman, Janosch Preuss, Tim van Beeck
https://arxiv.org/abs/2509.13108

Variational data assimilation for the wave equation in heterogeneous media: Numerical investigation of stability
In recent years, several numerical methods for solving the unique continuation problem for the wave equation in a homogeneous medium with given data on the lateral boundary of the space-time cylinder have been proposed. This problem enjoys Lipschitz stability if the geometric control condition is fulfilled, which allows devising optimally convergent numerical methods. In this article, we investigate whether these results carry over to the case in which the medium exhibits a jump discontinuity. …