On the new Narayana polynomials, the Gauss Narayana numbers and their polynomials
Engi̇n Özkan, Bahar Kuloğlu
Abstract
We give a new definition of Narayana polynomials and show that there is a relationship between the coefficient of the new Narayana polynomials and Pascal’s triangle. We define the Gauss Narayana numbers and their polynomials. Then we show that there is a relationship between the Gauss Narayana polynomials and the new Narayana polynomials. Also, we show that there is a relationship between the derivatives of the new Narayana polynomials and Pascal’s triangle. We also explain the relationship between the new Narayana polynomials and the known Pell numbers. Finally, we give the Hankel transform of the new Narayana polynomials.
Topics & Concepts
MathematicsWilson polynomialsOrthogonal polynomialsDiscrete orthogonal polynomialsClassical orthogonal polynomialsDifference polynomialsJacobi polynomialsHahn polynomialsPascal (unit)Gegenbauer polynomialsGaussMacdonald polynomialsPure mathematicsCombinatoricsDiscrete mathematicsComputer sciencePhysicsQuantum mechanicsProgramming languageAdvanced Mathematical Theories and ApplicationsAdvanced Mathematical IdentitiesMolecular spectroscopy and chirality