Certain properties and applications of the mixed degenerate Gould-Hopper type polynomials in mathematical physics

Abstract This paper presents a systematic study of the mixed degenerate Gould–Hopper type polynomials, beginning with their generating functions and fundamental operational properties. Summation identities, addition formulas, and a determinant representation are developed to reveal the underlying algebraic structure. A computational investigation of the zero distributions is carried out, supported by numerical illustrations and pattern analysis. The results provide insight into the analytical behavior of the family and its structural richness. Concluding remarks discuss theoretical implications and potential directions including asymptotics, orthogonality, and applications in mathematical physics.