I would like to know if the following recurrence relation is solvable
\begin{equation} (\alpha_{1}n^{2}+\beta_{1}n+\gamma_{1})\ c(n+1)+(\alpha_{0}n^{2}+\beta_{0}n+\gamma_{0})\ c(n)+(\alpha_{-1}n^{2}+\beta_{-1}n+\gamma_{-1})\ c(n-1)=0 \end{equation}
where $\alpha$'s,$\beta$'s and $\gamma$'s are constants.
I am particularly interested in the case where $\alpha_{1}=0$ and $\gamma_{-1}=0$. Moreover, $\beta_{1}=\alpha_{-1}$ and $\gamma_{1}=\beta_{-1}$ therefore the recurrence relation reduces to
\begin{equation} (\beta_{1}n+\gamma_{1})\ c(n+1)+(\alpha_{0}n^{2}+\beta_{0}n+\gamma_{0})\ c(n)+n(\beta_{1}n+\gamma_{1})\ c(n-1)=0 \end{equation}
I am hoping that I could find a similar recurrence relation for some special functions such as Hypergeometric functions or generalized Hypergeometric functions or Heun functions. Also, I know that some orthogonal polynomials such as Hahn, Krawtchoul and Charlier polynomials have three term recurrence relations. However, I have not been successful to match any of them with my recurrence relation.