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math.CV2026
On a multiplicative perturbation of Laguerre polynomials
Julien Grivaux
In this article, we study the family of polynomials \[ P_n(s, z)=\sum_{k=0}^n s^{(k)} z^{n-k} \] for . We prove that its roots are simple, and provide a precise localisation o…
math.CV2025
Duality, polarity and convolution in umbral calculus
Julien Grivaux
In this paper, we revisit foundations of umbral calculus using a straightforward approach based on an explicit matrix realization of binomial convolution. We construct an umbral du…
math.CV2016★ 3 cited
Tian's invariant of the Grassmann manifold
Julien Grivaux
We prove that Tian's invariant on the complex Grassmann manifold is equal to .