On $\delta$ -semiclassical orthogonal polynomials

  • K. H. Kwon (Department of Mathematics KAIST, Taejon 305-701) ;
  • Lee, D. W. (Department of Mathematics KAIST, Taejon 305-701) ;
  • Park, S. B. (Department of Mathematics Korea Military Academy, Seoul 139-799)
  • Published : 1997.02.01

Abstract

Consider an oparator equation of the form : $$ (1.1) H[y](x) = \alpha(x)\delta^2 y(x) + \beta(x)\delta y(x) = \lambda_n y(x), $$ where $\alphs(x)$ and $\beta(x)$ are polynomials of degree at most two and one respectively, $\lambda_n$ is the eigenvalue parameter, and $\delta$ is Hahn's operator $$ (1.2) \delta f(x) = \frac{(q - 1)x + \omega}{f(qx + \omega) - f(x)}, $$ for real constants $q(\neq \pm 1)$ and $\omega$.

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