Incomplete 2D Hermite polynomials: properties and applications

Incomplete forms of two-variable two-index Hermite polynomials are introduced. Their link with Laguerre polynomials is discussed and it is shown that they are a useful tool to study quantum mechanical harmonic oscillator entangled states. The possibility of developing the theory of complete 2D Hermite polynomials from the point of view of the incomplete forms is analyzed too. The orthogonality properties of the associated harmonic-oscillator functions are finally discussed.  2003 Elsevier Inc. All rights reserved