Certain Summation and Operational Formulas Involving Gould–Hopper–Lambda Polynomials

This manuscript introduces the family of Gould–Hopper–Lambda polynomials and establishes their quasi-monomial properties through the umbral method. This approach serves as a powerful mechanism to analyze the characteristic of multi-variable special polynomials. Several summation formulas for these polynomials are explored, and their operational identities are obtained using partial differential equations. The corresponding results for Hermite–Lambda polynomials are also obtained. In addition, a conclusion is given.