Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4633192 | Applied Mathematics and Computation | 2008 | 7 Pages |
Abstract
Both univariate and multivariate generalized Hermite polynomials are defined by introducing second order exponential differential operator, corresponding probabilistic expressions are given explicitly. Based on those expectation expressions, their generating functions, recursion relations and other properties are derived conveniently in connection to Stein's identities. In particular, orthogonality are investigated and associated expressions are presented accordingly. Additionally, some other classical identities related to Hermite polynomials are proved by an alternative way, and some examples and remarks are presented.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Zhengyuan Wei, Xinsheng Zhang,