Multiindex multivariable Hermite polynomials (Q701381)

The main results of the present paper involve multiindex and multivariable Hermite polynomials. The author first defines and obtains the basic properties, differential and pure recurrence relations, differential equations, generating function relations and expansions of 2-index, 2-variable Hermite polynomials and then gives corresponding results for the \(p\)-index, \(p\)-variable Hermite polynomials. Certain simpler results follow as special cases of the main findings of the paper.