Generating functions for relatives of classical polynomials

Abstract:

For several classical polynomials ${u_n}(x)$ satisfying a second order linear differential equation ${D_n}(x)$, there is a generating function $u(x,t) = \sum \nolimits _{n = 0}^\infty {{u_n}(x){t^n}}$. We provide expansions $\upsilon (x,t) = \sum \nolimits _{n = 0}^\infty {{\upsilon _n}(x){t^n}}$ where ${\upsilon _n}(x)$ is a second solution of ${D_n}(x)$.