New relations for two-dimensional Hermite polynomials
High Energy Physics - Theory
2009-10-22 v1 Classical Analysis and ODEs
Abstract
The effective formulas reducing the two-dimensional Hermite polynomials to the classical (one-dimensional) orthogonal polynomials are given. New one-parameter generating functions for these polynomials are derived. Asymptotical formulas for large values of indices are found. The applications to the squeezed one-mode states and to the time-dependent quantum harmonic oscillator are considered.
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Cite
@article{arxiv.hep-th/9312012,
title = {New relations for two-dimensional Hermite polynomials},
author = {V. V. Dodonov and V. I. Man'ko},
journal= {arXiv preprint arXiv:hep-th/9312012},
year = {2009}
}
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17 pages