Generating Functions for Products of Special Laguerre 2D and Hermite 2D Polynomials

• 作者: Alfred Wü nsche
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: LAGUERRE and HERMITE POLYNOMIALS LAGUERRE 2D POLYNOMIALS JACOBI POLYNOMIALS Mehler Formula SU(1 1) Operator DISENTANGLEMENT Gaussian CONVOLUTIONS
• 年，卷（期）: 2015,（12）
• 页码范围: 2142-2168
• 页数: 27页
• 分类号: O1

摘要

The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polynomials. Furthermore, the generating function for mixed products of Laguerre 2D and Hermite 2D polynomials and for products of two Hermite 2D polynomials is calculated. A set of infinite sums over products of two Laguerre 2D polynomials as intermediate step to the generating function for products of Laguerre 2D polynomials is evaluated but these sums possess also proper importance for calculations with Laguerre polynomials. With the technique of operator disentanglement some operator identities are derived in an appendix. They allow calculating convolutions of Gaussian functions combined with polynomials in one- and two-dimensional case and are applied to evaluate the discussed generating functions.