Abstract
The effective formulas reducing the two-dimensional Hermite polynomials to the classical one-dimensional orthogonal polynomials by Jacobi, Gegenbauer, Legendre, Laguerre, and Hermite are given. New one-parameter generating functions for the ‘‘diagonal’’ multidimensional Hermite polynomials are derived. The factorial moments and cumulants of the distribution functions related to the Hermite polynomials of two variables with equal indices are expressed in terms of the Legendre and Chebyshev polynomials. Asymptotical formulas for the two-dimensional polynomials with large values of indices and zero arguments are found. The applications to the squeezed one-mode states and to the time-dependent quantum harmonic oscillator are considered.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
