On a system of partial differential equations and the bivariate Hermite polynomials
| Autor: | Zhi-Guo Liu |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Hermite polynomials Applied Mathematics Discrete orthogonal polynomials 010102 general mathematics Mathematics::Classical Analysis and ODEs Mehler–Heine formula 01 natural sciences 010305 fluids & plasmas Classical orthogonal polynomials Algebra Difference polynomials Hermite interpolation 0103 physical sciences Orthogonal polynomials Laguerre polynomials 0101 mathematics Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 454:1-17 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2017.04.066 |
| Popis: | Using the theory of analytic functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of partial differential equations, then, it can be expanded in terms of the product of the bivariate Hermite polynomials. This expansion theorem allows us to develop a systematic method to prove the identities involving the bivariate Hermite polynomials. With this expansion theorem, we can easily derive, among others, the Mehler formula, Nielsen's formulas, Doetsch's formula, the addition formula, Weisner's formulas, Carlitz's formulas for the bivariate Hermite polynomials. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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