Truncated Hermite polynomials

2022/08/01 by Diego Dominici, Dominici, Diego, Francisco Marcellán +1 · 1 citation
Chemical Engineering · Mathematics · #33C45 #33C47 (primary) #60E05 (secondary) #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical functions and polynomials #Thermodynamic properties of mixtures

paper · pdf · doi:10.48550/arxiv.2208.01125

openalex publication_date 2022/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the family of polynomials p_n( x;z) , orthogonal with respect to the inner product ⟨ f,g⟩ = ∫_-z^z f( x) g( x) e^-x² dx. We show some properties about the coefficients in their 3-term recurrence relation, connections between p_n( x;z) and p_n^′( x;z) , a second order differential equation satisfied by p_n( x;z) , and an electrostatic interpretation of their zeros.

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