Degenerate Versions of Hypergeometric Bernoulli–Euler Polynomials
Clemente Cesarano, Yamilet Quintana, William Ramírez
Abstract
In this paper, we introduce degenerate versions of the hypergeometric Bernoulli and Euler polynomials. We demonstrate that they form $$\Delta_{\lambda}$$ –Appell sets and provide some of their algebraic properties, including inversion formulas, as well as the associated matrix formulation. Additionally, we focus our attention on the monomiality principle associated with them and determine the corresponding derivative and multiplicative operators.
Topics & Concepts
MathematicsDegenerate energy levelsPure mathematicsEuler's formulaHypergeometric functionHypergeometric distributionAlgebra over a fieldBasic hypergeometric seriesBernoulli's principleMathematical analysisAerospace engineeringQuantum mechanicsEngineeringPhysicsAdvanced Mathematical IdentitiesMathematical functions and polynomialsPolynomial and algebraic computation