Abstract
A general class of the 2-variable polynomials is considered, and its properties are derived. Further, these polynomials are used to introduce the 2-variable general-Appell polynomials (2VgAP). The generating function for the 2VgAP is derived, and a correspondence between these polynomials and the Appell polynomials is established. The differential equation, recurrence relations, and other properties for the 2VgAP are obtained within the context of the monomiality principle. This paper is the first attempt in the direction of introducing a new family of special polynomials, which includes many other new special polynomial families as its particular cases.
Highlights
Introduction and PreliminariesThe Appell polynomials are very often found in different applications in pure and applied mathematics
We recall that the 2-variable Hermite Kampede Feriet polynomials (2VHKdFP) Hn(x, y) [18], the Gould-Hopper polynomials (GHP) Hn(m)(x, y) [19], and the Hermite-Appell polynomials (HAP) HAn(x, y) [20] are defined by the generating functions ext+yt2
In view of generating functions (14), (16), (17), and (18), we note that the 2VHKdFP Hn(x, y), the GHP Hn(m)(x, y), and the HAP HAn(x, y) belong to 2-variable general polynomial (2VgP) family
Summary
Introduction and PreliminariesThe Appell polynomials are very often found in different applications in pure and applied mathematics. These polynomials are used to introduce the 2-variable general-Appell polynomials (2VgAP). The generating function for the 2VgAP is derived, and a correspondence between these polynomials and the Appell polynomials is established. (eα1 t α1α2 ⋅ ⋅ ⋅ αmtm − 1) (eα2t − 1) ⋅ ⋅ ⋅
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