Differential Equations Associated with Two Variable Degenerate Hermite Polynomials
Kyung-Won Hwang, C. S. Ryoo
Abstract
In this paper, we introduce the two variable degenerate Hermite polynomials and obtain some new symmetric identities for two variable degenerate Hermite polynomials. In order to give explicit identities for two variable degenerate Hermite polynomials, differential equations arising from the generating functions of degenerate Hermite polynomials are studied. Finally, we investigate the structure and symmetry of the zeros of the two variable degenerate Hermite equations.
Topics & Concepts
Hermite polynomialsDegenerate energy levelsMathematicsVariable (mathematics)Classical orthogonal polynomialsDifference polynomialsPure mathematicsOrthogonal polynomialsDifferential equationDiscrete orthogonal polynomialsWilson polynomialsMathematical analysisPhysicsQuantum mechanicsNonlinear Waves and SolitonsAdvanced Mathematical IdentitiesFractional Differential Equations Solutions