Identities involving 3-variable Hermite polynomials arising from umbral method

Abstract

Abstract In this paper, we employ an umbral method to reformulate the 3-variable Hermite polynomials and introduce the 4-parameter 3-variable Hermite polynomials. We also obtain some new properties for these polynomials. Moreover, some special cases are discussed and some concluding remarks are also given.

Keywords

• Umbral method (umbra)
• 3-variable generalised Hermite polynomials
• 4-parameter 3-variable Hermite polynomials
• Generating function