Properties of certain new special polynomials associated with Sheffer sequences

Abstract

In this article, the Laguerre-Gould Hopper polynomials are combined with Sheffer sequences to introduce certain mixed type special polynomials. Certain important properties of these polynomials are established. Further, operational and integral representations for these mixed polynomials are derived.

Some results on hybrid relatives of the Sheffer polynomials via operational rules

“…Proof. We recall the following equations [5]: Performing the operation ( ) on equations (2.11) and (2.12) and using recurrence relation (2.8), we obtain assertions (2.9) and (2.10).…”

“…al. [5] introduced the Laguerre-Gould-Hopper-Sheffer polynomials (LGHSP) L H .m;r/ s n .x; y;´/ which are defined by the following generating function:…”

“…The following operational representations for the LGHSP L H .m;r/ s n .x; y;´/ hold [5]: For suitable choices of the variables and indices the LGHSP L H .m;r/ s n .x; y;´/ reduce to certain hybrid special polynomials. These polynomials along with their notation and name are mentioned in Table 1.…”

Relevance of Factorization Method to Differential and Integral Equations Associated with Hybrid Class of Polynomials

“…In 2016, Raza et al [7] presented a new class of Laguerre-Gould-Hopper-Sheffer polynomials (3VLGHSP) L H (p,s) S n (a, b, c) by using the generating function. The development and properties of hybrid special polynomials [8][9][10] have been most substantial theme in applied mathematics in last decades.…”

“…The development and properties of hybrid special polynomials [8][9][10] have been most substantial theme in applied mathematics in last decades. The generating function of Laguerre-Gould-Hopper-Sheffer polynomials (3VLGHSP) L H (p,s) n S n (a, b, c) [7] can be given as follows…”