• Korean Journal of Mathematics
• /
• v.25 no.2
• /
• pp.181-199
• /
• 2017

In this paper we consider the orthogonal polynomials with weights ${\omega}_{\alpha}(x)=x^{\alpha}{\exp}(-x^3+tx)$ and $W_{\alpha}(x)={\mid}x{\mid}^{2{\alpha}+1}{\exp}(-x^6+tx^2)$. Using the compatibility conditions for the ladder operators for these orthogonal polynomials, we derive several difference equations satisfied by the recurrence coefficients of these orthogonal polynomials. We also derive differential-difference equations and second order linear ordinary differential equations satisfied by these orthogonal polynomials.