New identities about operator Hermite polynomials and their related integration formulas

2010/12/02 by Hong-Yi Fan, Fan, Hong-Yi, Hong‐Chun Yuan +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Iterative Methods for Nonlinear Equations #Quantum Information and Cryptography #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.1012.0437

7 pages

arxiv created 2010/12/02 · openalex publication_date 2010/12/02 · arxiv updated 2010/12/03 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

By virtue of the technique of integration within an ordered product (IWOP) of operators and the bipartite entangled state representation we derive some new identities about operator Hermite polynomials in both single- and two-variable, we also find a binomial-like theorem between the single-variable Hermite polynomials and the two-variable Hermite polynomials. Application of these identities in deriving new integration formulas, but without really doing the integration in the usual sense, is demonstrated.

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