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This is a Quantitative Study study (also classified as: Experimental Study).

October 11, 2025Open Access

Generalization of Sheffer-λ polynomials

Puntos clave

A new generalization of sheffer-lambda polynomials is proposed, taking advantage of existing polynomial families.
Explicit forms, summation formulas, and basic properties, such as quasi-monomiality and differential equations, are derived.
3D graphs depict the distribution of real roots for both the main family and its subfamilies, enhancing understanding.
Twice iterated sheffer-lambda polynomials are defined, with similar properties and visual representations investigated.

Resumen

Abstract The aim of this study is to define a new generalization of Sheffer- λ polynomials with the help of Sheffer polynomials and λ -polynomials. For this family, explicit form, summation formulas, quasi-monomiality properties, differential equation and determinant representation are obtained. Subfamilies of these polynomials are introduced and similar properties for subfamilies are found. In addition, 3D graphs and the distribution of real roots are plotted for these subfamilies. Similarly, twice iterated Sheffer- λ polynomials are defined and basic properties for this family and its subfamilies are obtained, and 3D graphs and the distribution of real roots are also investigated for the subfamilies.

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