A new generalization of Laguerre-based Appell polynomials with two parameters

Key Points

• To define and explore a new generalization of Laguerre-based Appell polynomials with two parameters.
• Defined a new family of Laguerre-based Appell polynomials
• Established a recurrence relation and a lowering operator
• Developed an integro-partial differential equation
• Introduced subpolynomials, including Laguerre-based Hermite-Frobenius Euler and Miller-Lee polynomials
• Visualized 3D graphs of subfamilies and their real root distributions.
• Derived various properties of the new polynomial family
• Visual representations of the subpolynomials and their real roots were created
• Demonstrated connections between Laguerre-based polynomials and harmonic analysis.

Abstract